From 1f5281b19d7f3ad29db9d9cfbb3979fc72691b5e Mon Sep 17 00:00:00 2001
From: Luke Videckis <lrvideckis@gmail.com>
Date: Sun, 3 Aug 2025 15:23:53 -0600
Subject: [PATCH 01/21] different style + nits

---
 .../data_structures/uncommon/linear_rmq.hpp   | 44 +++++++++----------
 .../data_structures/rmq_linear.test.cpp       |  8 ++--
 2 files changed, 26 insertions(+), 26 deletions(-)

diff --git a/library/data_structures/uncommon/linear_rmq.hpp b/library/data_structures/uncommon/linear_rmq.hpp
index 503308a8..cb1ada24 100644
--- a/library/data_structures/uncommon/linear_rmq.hpp
+++ b/library/data_structures/uncommon/linear_rmq.hpp
@@ -1,10 +1,10 @@
 #pragma once
 //! https://codeforces.com/blog/entry/125371?#comment-1173604
 //! @code
-//!   linear_rmq rmq1(a, less());//right-most min
-//!   linear_rmq rmq2(a, less_equal());//left-most min
-//!   linear_rmq rmq3(a, greater());//right-most max
-//!   linear_rmq rmq4(a, greater_equal());//left-most max
+//!   linear_rmq rmq1(a, less());          //right-most min
+//!   linear_rmq rmq2(a, less_equal());    //left-most min
+//!   linear_rmq rmq3(a, greater());       //right-most max
+//!   linear_rmq rmq4(a, greater_equal()); //left-most max
 //!   linear_rmq rmq5(a, [&](auto& x, auto& y) {
 //!     return x < y;
 //!   });
@@ -12,38 +12,38 @@
 //! @time O(n + q)
 //! @space O(n)
 template<class T, class F> struct linear_rmq {
+  int n;
   vector<T> a;
   F cmp;
-  vi head;
-  vector<array<int, 2>> t;
+  vi asc, in, head;
   linear_rmq(const vector<T>& a, F cmp):
-    a(a), cmp(cmp), head(sz(a) + 1), t(sz(a)) {
+    n(sz(a)), a(a), cmp(cmp), asc(n), in(n), head(n + 1) {
     vi st{-1};
-    for (int i = 0; i <= sz(a); i++) {
+    rep(i, 0, n + 1) {
       int prev = -1;
       while (st.back() != -1 &&
-        (i == sz(a) || !cmp(a[st.back()], a[i]))) {
+        (i == n || !cmp(a[st.back()], a[i]))) {
         if (prev != -1) head[prev] = st.back();
-        int pw2 = 1 << __lg((end(st)[-2] + 1) ^ i);
-        t[st.back()][0] = prev = i & -pw2;
+        int pw2 = bit_floor((end(st)[-2] + 1u) ^ i);
+        in[st.back()] = prev = i & -pw2;
         st.pop_back();
-        t[st.back() + 1][1] |= pw2;
+        asc[st.back() + 1] |= pw2;
       }
       if (prev != -1) head[prev] = i;
       st.push_back(i);
     }
-    rep(i, 1, sz(a)) t[i][1] =
-      (t[i][1] | t[i - 1][1]) & -(t[i][0] & -t[i][0]);
+    rep(i, 1, n) asc[i] =
+      (asc[i] | asc[i - 1]) & -(in[i] & -in[i]);
   }
-  int query_idx(int l, int r) { // [l, r]
-    if (unsigned j = t[l][0] ^ t[r][0]; j) {
-      j = t[l][1] & t[r][1] & -bit_floor(j);
-      if (unsigned k = t[l][1] ^ j; k)
-        k = bit_floor(k), l = head[(t[l][0] & -k) | k];
-      if (unsigned k = t[r][1] ^ j; k)
-        k = bit_floor(k), r = head[(t[r][0] & -k) | k];
+  int idx(int l, int r) { // [l, r]
+    if (unsigned j = in[l] ^ in[r]; j) {
+      j = asc[l] & asc[r] & -bit_floor(j);
+      if (unsigned k = asc[l] ^ j; k)
+        k = bit_floor(k), l = head[(in[l] & -k) | k];
+      if (unsigned k = asc[r] ^ j; k)
+        k = bit_floor(k), r = head[(in[r] & -k) | k];
     }
     return cmp(a[l], a[r]) ? l : r;
   }
-  T query(int l, int r) { return a[query_idx(l, r)]; }
+  T query(int l, int r) { return a[idx(l, r)]; }
 };
diff --git a/tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp b/tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp
index 90a06dcf..87354eca 100644
--- a/tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp
+++ b/tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp
@@ -16,21 +16,21 @@ int main() {
   while (q--) {
     int l, r;
     cin >> l >> r;
-    int idx_right_min = rmq_less.query_idx(l, r - 1);
+    int idx_right_min = rmq_less.idx(l, r - 1);
     assert(idx_right_min + 1 == r ||
       rmq_less.query(idx_right_min + 1, r - 1) >
         a[idx_right_min]);
     assert(l <= idx_right_min && idx_right_min < r);
     assert(rmq_less.query(l, r - 1) == a[idx_right_min]);
     assert(
-      idx_right_min == rmq_greater.query_idx(l, r - 1));
-    int idx_left_min = rmq_less_equal.query_idx(l, r - 1);
+      idx_right_min == rmq_greater.idx(l, r - 1));
+    int idx_left_min = rmq_less_equal.idx(l, r - 1);
     assert(l == idx_left_min ||
       rmq_less_equal.query(l, idx_left_min - 1) >
         a[idx_left_min]);
     assert(l <= idx_left_min && idx_left_min < r);
     assert(idx_left_min ==
-      rmq_greater_equal.query_idx(l, r - 1));
+      rmq_greater_equal.idx(l, r - 1));
     assert(a[idx_right_min] == a[idx_left_min]);
     assert(idx_left_min <= idx_right_min);
     cout << a[idx_right_min] << '\n';

From 9e9d53915ae0f7e2cc72dc7eb536cb40748dcd77 Mon Sep 17 00:00:00 2001
From: GitHub <noreply@github.com>
Date: Sun, 3 Aug 2025 21:35:53 +0000
Subject: [PATCH 02/21] [auto-verifier] verify commit
 1f5281b19d7f3ad29db9d9cfbb3979fc72691b5e

---
 .verify-helper/timestamps.remote.json | 15 ++++++---------
 1 file changed, 6 insertions(+), 9 deletions(-)

diff --git a/.verify-helper/timestamps.remote.json b/.verify-helper/timestamps.remote.json
index 904dc3cf..97c8b734 100644
--- a/.verify-helper/timestamps.remote.json
+++ b/.verify-helper/timestamps.remote.json
@@ -33,15 +33,14 @@
 "tests/library_checker_aizu_tests/data_structures/line_tree_lib_checker.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/data_structures/merge_sort_tree.test.cpp": "2025-02-11 13:53:30 -0700",
 "tests/library_checker_aizu_tests/data_structures/mode_query.test.cpp": "2025-02-10 23:30:47 -0700",
-"tests/library_checker_aizu_tests/data_structures/permutation_tree.test.cpp": "2025-06-03 13:37:20 -0600",
 "tests/library_checker_aizu_tests/data_structures/persistent_queue_tree.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/persistent_seg_tree.test.cpp": "2024-12-05 10:41:42 -0600",
 "tests/library_checker_aizu_tests/data_structures/pq_ds_undo_sliding_window.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/pq_ds_undo_with_dsu.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/range_parallel_dsu.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/data_structures/rmq_disjoint_sparse_table.test.cpp": "2024-12-15 14:34:10 -0600",
-"tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp": "2025-06-03 13:37:20 -0600",
-"tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2025-06-03 13:37:20 -0600",
+"tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp": "2025-08-03 15:23:53 -0600",
+"tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2025-08-03 15:23:53 -0600",
 "tests/library_checker_aizu_tests/data_structures/rmq_sparse_table_inc.test.cpp": "2024-12-15 14:34:10 -0600",
 "tests/library_checker_aizu_tests/data_structures/simple_tree.test.cpp": "2024-12-14 15:47:13 -0600",
 "tests/library_checker_aizu_tests/data_structures/simple_tree_inc.test.cpp": "2024-12-21 00:23:10 -0500",
@@ -78,8 +77,6 @@
 "tests/library_checker_aizu_tests/handmade_tests/mobius.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/mod_int.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/n_choose_k.test.cpp": "2025-01-15 00:22:31 -0700",
-"tests/library_checker_aizu_tests/handmade_tests/permutation_tree_small.test.cpp": "2025-06-03 13:37:20 -0600",
-"tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp": "2025-06-03 13:37:20 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/sa_find_subarray.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/seg_tree_find.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/seg_tree_find_small.test.cpp": "2024-12-14 19:50:29 -0600",
@@ -107,9 +104,9 @@
 "tests/library_checker_aizu_tests/math/xor_basis.test.cpp": "2025-04-22 21:37:22 -0500",
 "tests/library_checker_aizu_tests/math/xor_basis_intersection.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_binary_tree.test.cpp": "2025-02-10 14:50:36 -0700",
-"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_k_ary_tree.test.cpp": "2025-06-03 13:37:20 -0600",
-"tests/library_checker_aizu_tests/monotonic_stack_related/count_rectangles.test.cpp": "2025-06-03 13:37:20 -0600",
-"tests/library_checker_aizu_tests/monotonic_stack_related/max_rect_histogram.test.cpp": "2025-06-03 13:37:20 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_k_ary_tree.test.cpp": "2025-08-03 15:23:53 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/count_rectangles.test.cpp": "2025-08-03 15:23:53 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/max_rect_histogram.test.cpp": "2025-08-03 15:23:53 -0600",
 "tests/library_checker_aizu_tests/strings/kmp.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/strings/lcp_array.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/lcp_query_palindrome.test.cpp": "2025-02-10 14:50:36 -0700",
@@ -123,7 +120,7 @@
 "tests/library_checker_aizu_tests/strings/sa_cmp.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/sa_sort_pairs.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/single_matching_bs.test.cpp": "2025-02-10 14:50:36 -0700",
-"tests/library_checker_aizu_tests/strings/suffix_array.test.cpp": "2025-06-03 13:37:20 -0600",
+"tests/library_checker_aizu_tests/strings/suffix_array.test.cpp": "2025-08-03 15:23:53 -0600",
 "tests/library_checker_aizu_tests/strings/suffix_array_short.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/trie.test.cpp": "2024-12-05 10:41:42 -0600",
 "tests/library_checker_aizu_tests/strings/wildcard_pattern_matching.test.cpp": "2024-12-14 19:50:29 -0600",

From 278d08561eae60094da18ea3592ef093bd705d3e Mon Sep 17 00:00:00 2001
From: Luke Videckis <lrvideckis@gmail.com>
Date: Sun, 3 Aug 2025 15:40:30 -0600
Subject: [PATCH 03/21] fixes

---
 library/data_structures/uncommon/linear_rmq.hpp        | 10 +++++-----
 library/data_structures/uncommon/permutation_tree.hpp  |  4 ++--
 .../handmade_tests/rmq_small_n.test.cpp                |  2 +-
 3 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/library/data_structures/uncommon/linear_rmq.hpp b/library/data_structures/uncommon/linear_rmq.hpp
index cb1ada24..629aa40c 100644
--- a/library/data_structures/uncommon/linear_rmq.hpp
+++ b/library/data_structures/uncommon/linear_rmq.hpp
@@ -24,16 +24,16 @@ template<class T, class F> struct linear_rmq {
       while (st.back() != -1 &&
         (i == n || !cmp(a[st.back()], a[i]))) {
         if (prev != -1) head[prev] = st.back();
-        int pw2 = bit_floor((end(st)[-2] + 1u) ^ i);
-        in[st.back()] = prev = i & -pw2;
+        int b = bit_floor((end(st)[-2] + 1u) ^ i);
+        in[st.back()] = prev = i & -b;
         st.pop_back();
-        asc[st.back() + 1] |= pw2;
+        asc[st.back() + 1] |= b;
       }
       if (prev != -1) head[prev] = i;
       st.push_back(i);
     }
-    rep(i, 1, n) asc[i] =
-      (asc[i] | asc[i - 1]) & -(in[i] & -in[i]);
+    rep(i, 1, n)(asc[i] |= asc[i - 1]) &=
+      -(in[i] & -in[i]);
   }
   int idx(int l, int r) { // [l, r]
     if (unsigned j = in[l] ^ in[r]; j) {
diff --git a/library/data_structures/uncommon/permutation_tree.hpp b/library/data_structures/uncommon/permutation_tree.hpp
index fbd98057..e5553677 100644
--- a/library/data_structures/uncommon/permutation_tree.hpp
+++ b/library/data_structures/uncommon/permutation_tree.hpp
@@ -37,8 +37,8 @@ struct perm_tree {
       linear_rmq rmq_min(a_inv, less());
       linear_rmq rmq_max(a_inv, greater());
       rep(i, 1, n) {
-        mn_i[i] = a_inv[rmq_min.query_idx(a[i - 1], a[i])];
-        mx_i[i] = a_inv[rmq_max.query_idx(a[i - 1], a[i])];
+        mn_i[i] = a_inv[rmq_min.idx(a[i - 1], a[i])];
+        mx_i[i] = a_inv[rmq_max.idx(a[i - 1], a[i])];
       }
     }
     rep(i, 0, n) allocate(i, a[i], 1, 0, {});
diff --git a/tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp b/tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp
index 8b97202f..2dbec0e4 100644
--- a/tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp
+++ b/tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp
@@ -13,7 +13,7 @@ void test_all_subarrays(const vector<int>& a) {
   linear_rmq lin_rmq(a, less());
   for (int l = 0; l < n; l++) {
     for (int r = l + 1; r <= n; r++) {
-      int idx_min = lin_rmq.query_idx(l, r - 1);
+      int idx_min = lin_rmq.idx(l, r - 1);
       assert(l <= idx_min && idx_min < r);
       assert(a[idx_min] == rmq.query(l, r));
       assert(a[idx_min] == dis_rmq.query(l, r));

From d32ef9bb956a9f8bde70833e25aaee035f8c1e82 Mon Sep 17 00:00:00 2001
From: GitHub <noreply@github.com>
Date: Sun, 3 Aug 2025 21:54:33 +0000
Subject: [PATCH 04/21] [auto-verifier] verify commit
 278d08561eae60094da18ea3592ef093bd705d3e

---
 .verify-helper/timestamps.remote.json | 15 +++++++++------
 1 file changed, 9 insertions(+), 6 deletions(-)

diff --git a/.verify-helper/timestamps.remote.json b/.verify-helper/timestamps.remote.json
index 97c8b734..38de785e 100644
--- a/.verify-helper/timestamps.remote.json
+++ b/.verify-helper/timestamps.remote.json
@@ -33,14 +33,15 @@
 "tests/library_checker_aizu_tests/data_structures/line_tree_lib_checker.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/data_structures/merge_sort_tree.test.cpp": "2025-02-11 13:53:30 -0700",
 "tests/library_checker_aizu_tests/data_structures/mode_query.test.cpp": "2025-02-10 23:30:47 -0700",
+"tests/library_checker_aizu_tests/data_structures/permutation_tree.test.cpp": "2025-08-03 15:40:30 -0600",
 "tests/library_checker_aizu_tests/data_structures/persistent_queue_tree.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/persistent_seg_tree.test.cpp": "2024-12-05 10:41:42 -0600",
 "tests/library_checker_aizu_tests/data_structures/pq_ds_undo_sliding_window.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/pq_ds_undo_with_dsu.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/range_parallel_dsu.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/data_structures/rmq_disjoint_sparse_table.test.cpp": "2024-12-15 14:34:10 -0600",
-"tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp": "2025-08-03 15:23:53 -0600",
-"tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2025-08-03 15:23:53 -0600",
+"tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp": "2025-08-03 15:40:30 -0600",
+"tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2025-08-03 15:40:30 -0600",
 "tests/library_checker_aizu_tests/data_structures/rmq_sparse_table_inc.test.cpp": "2024-12-15 14:34:10 -0600",
 "tests/library_checker_aizu_tests/data_structures/simple_tree.test.cpp": "2024-12-14 15:47:13 -0600",
 "tests/library_checker_aizu_tests/data_structures/simple_tree_inc.test.cpp": "2024-12-21 00:23:10 -0500",
@@ -77,6 +78,8 @@
 "tests/library_checker_aizu_tests/handmade_tests/mobius.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/mod_int.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/n_choose_k.test.cpp": "2025-01-15 00:22:31 -0700",
+"tests/library_checker_aizu_tests/handmade_tests/permutation_tree_small.test.cpp": "2025-08-03 15:40:30 -0600",
+"tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp": "2025-08-03 15:40:30 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/sa_find_subarray.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/seg_tree_find.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/seg_tree_find_small.test.cpp": "2024-12-14 19:50:29 -0600",
@@ -104,9 +107,9 @@
 "tests/library_checker_aizu_tests/math/xor_basis.test.cpp": "2025-04-22 21:37:22 -0500",
 "tests/library_checker_aizu_tests/math/xor_basis_intersection.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_binary_tree.test.cpp": "2025-02-10 14:50:36 -0700",
-"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_k_ary_tree.test.cpp": "2025-08-03 15:23:53 -0600",
-"tests/library_checker_aizu_tests/monotonic_stack_related/count_rectangles.test.cpp": "2025-08-03 15:23:53 -0600",
-"tests/library_checker_aizu_tests/monotonic_stack_related/max_rect_histogram.test.cpp": "2025-08-03 15:23:53 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_k_ary_tree.test.cpp": "2025-08-03 15:40:30 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/count_rectangles.test.cpp": "2025-08-03 15:40:30 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/max_rect_histogram.test.cpp": "2025-08-03 15:40:30 -0600",
 "tests/library_checker_aizu_tests/strings/kmp.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/strings/lcp_array.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/lcp_query_palindrome.test.cpp": "2025-02-10 14:50:36 -0700",
@@ -120,7 +123,7 @@
 "tests/library_checker_aizu_tests/strings/sa_cmp.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/sa_sort_pairs.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/single_matching_bs.test.cpp": "2025-02-10 14:50:36 -0700",
-"tests/library_checker_aizu_tests/strings/suffix_array.test.cpp": "2025-08-03 15:23:53 -0600",
+"tests/library_checker_aizu_tests/strings/suffix_array.test.cpp": "2025-08-03 15:40:30 -0600",
 "tests/library_checker_aizu_tests/strings/suffix_array_short.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/trie.test.cpp": "2024-12-05 10:41:42 -0600",
 "tests/library_checker_aizu_tests/strings/wildcard_pattern_matching.test.cpp": "2024-12-14 19:50:29 -0600",

From 03e2059c08f363df1b18692ac7b3afe8aec4b27d Mon Sep 17 00:00:00 2001
From: Luke Videckis <lrvideckis@gmail.com>
Date: Sun, 3 Aug 2025 17:11:36 -0600
Subject: [PATCH 05/21] format

---
 .../data_structures/rmq_linear.test.cpp                    | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp b/tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp
index 87354eca..fb3de419 100644
--- a/tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp
+++ b/tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp
@@ -22,15 +22,14 @@ int main() {
         a[idx_right_min]);
     assert(l <= idx_right_min && idx_right_min < r);
     assert(rmq_less.query(l, r - 1) == a[idx_right_min]);
-    assert(
-      idx_right_min == rmq_greater.idx(l, r - 1));
+    assert(idx_right_min == rmq_greater.idx(l, r - 1));
     int idx_left_min = rmq_less_equal.idx(l, r - 1);
     assert(l == idx_left_min ||
       rmq_less_equal.query(l, idx_left_min - 1) >
         a[idx_left_min]);
     assert(l <= idx_left_min && idx_left_min < r);
-    assert(idx_left_min ==
-      rmq_greater_equal.idx(l, r - 1));
+    assert(
+      idx_left_min == rmq_greater_equal.idx(l, r - 1));
     assert(a[idx_right_min] == a[idx_left_min]);
     assert(idx_left_min <= idx_right_min);
     cout << a[idx_right_min] << '\n';

From 93d2c19a1db18c29b7e49f21de8bcbfb19d36ce8 Mon Sep 17 00:00:00 2001
From: GitHub <noreply@github.com>
Date: Sun, 3 Aug 2025 23:13:37 +0000
Subject: [PATCH 06/21] [auto-verifier] verify commit
 03e2059c08f363df1b18692ac7b3afe8aec4b27d

---
 .verify-helper/timestamps.remote.json | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.verify-helper/timestamps.remote.json b/.verify-helper/timestamps.remote.json
index 38de785e..dccde6a1 100644
--- a/.verify-helper/timestamps.remote.json
+++ b/.verify-helper/timestamps.remote.json
@@ -40,7 +40,7 @@
 "tests/library_checker_aizu_tests/data_structures/pq_ds_undo_with_dsu.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/range_parallel_dsu.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/data_structures/rmq_disjoint_sparse_table.test.cpp": "2024-12-15 14:34:10 -0600",
-"tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp": "2025-08-03 15:40:30 -0600",
+"tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp": "2025-08-03 17:11:36 -0600",
 "tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2025-08-03 15:40:30 -0600",
 "tests/library_checker_aizu_tests/data_structures/rmq_sparse_table_inc.test.cpp": "2024-12-15 14:34:10 -0600",
 "tests/library_checker_aizu_tests/data_structures/simple_tree.test.cpp": "2024-12-14 15:47:13 -0600",

From 78b05a3be2b222872d0a9f642b4bbe7e21697469 Mon Sep 17 00:00:00 2001
From: Luke Videckis <lrvideckis@gmail.com>
Date: Sun, 3 Aug 2025 17:18:38 -0600
Subject: [PATCH 07/21] suppress

---
 tests/.config/.cppcheck_suppression_list | 1 +
 1 file changed, 1 insertion(+)

diff --git a/tests/.config/.cppcheck_suppression_list b/tests/.config/.cppcheck_suppression_list
index b49f37a0..a5be8a60 100644
--- a/tests/.config/.cppcheck_suppression_list
+++ b/tests/.config/.cppcheck_suppression_list
@@ -62,3 +62,4 @@ unusedFunction:../kactl/content/number-theory/ModPow.h:13
 unusedFunction:../kactl/stress-tests/utilities/genTree.h:49
 assertWithSideEffect:library_checker_aizu_tests/math/xor_basis_intersection.test.cpp:27
 assertWithSideEffect:library_checker_aizu_tests/math/xor_basis_intersection.test.cpp:36
+containerOutOfBounds:../library/data_structures/uncommon/permutation_tree.hpp:85

From 60546c3fcb51a77ee74daaf1c3258f7b820e0cd4 Mon Sep 17 00:00:00 2001
From: Luke Videckis <lrvideckis@gmail.com>
Date: Sun, 3 Aug 2025 17:30:02 -0600
Subject: [PATCH 08/21] another golf

---
 library/data_structures/uncommon/linear_rmq.hpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/library/data_structures/uncommon/linear_rmq.hpp b/library/data_structures/uncommon/linear_rmq.hpp
index 629aa40c..884bd532 100644
--- a/library/data_structures/uncommon/linear_rmq.hpp
+++ b/library/data_structures/uncommon/linear_rmq.hpp
@@ -21,7 +21,7 @@ template<class T, class F> struct linear_rmq {
     vi st{-1};
     rep(i, 0, n + 1) {
       int prev = -1;
-      while (st.back() != -1 &&
+      while (sz(st) > 1 &&
         (i == n || !cmp(a[st.back()], a[i]))) {
         if (prev != -1) head[prev] = st.back();
         int b = bit_floor((end(st)[-2] + 1u) ^ i);

From a2e47016dcd772c894b7fafef36b02ccb0473042 Mon Sep 17 00:00:00 2001
From: GitHub <noreply@github.com>
Date: Sun, 3 Aug 2025 23:44:05 +0000
Subject: [PATCH 09/21] [auto-verifier] verify commit
 60546c3fcb51a77ee74daaf1c3258f7b820e0cd4

---
 .verify-helper/timestamps.remote.json | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/.verify-helper/timestamps.remote.json b/.verify-helper/timestamps.remote.json
index dccde6a1..b63e01f6 100644
--- a/.verify-helper/timestamps.remote.json
+++ b/.verify-helper/timestamps.remote.json
@@ -33,15 +33,15 @@
 "tests/library_checker_aizu_tests/data_structures/line_tree_lib_checker.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/data_structures/merge_sort_tree.test.cpp": "2025-02-11 13:53:30 -0700",
 "tests/library_checker_aizu_tests/data_structures/mode_query.test.cpp": "2025-02-10 23:30:47 -0700",
-"tests/library_checker_aizu_tests/data_structures/permutation_tree.test.cpp": "2025-08-03 15:40:30 -0600",
+"tests/library_checker_aizu_tests/data_structures/permutation_tree.test.cpp": "2025-08-03 17:30:02 -0600",
 "tests/library_checker_aizu_tests/data_structures/persistent_queue_tree.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/persistent_seg_tree.test.cpp": "2024-12-05 10:41:42 -0600",
 "tests/library_checker_aizu_tests/data_structures/pq_ds_undo_sliding_window.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/pq_ds_undo_with_dsu.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/range_parallel_dsu.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/data_structures/rmq_disjoint_sparse_table.test.cpp": "2024-12-15 14:34:10 -0600",
-"tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp": "2025-08-03 17:11:36 -0600",
-"tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2025-08-03 15:40:30 -0600",
+"tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp": "2025-08-03 17:30:02 -0600",
+"tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2025-08-03 17:30:02 -0600",
 "tests/library_checker_aizu_tests/data_structures/rmq_sparse_table_inc.test.cpp": "2024-12-15 14:34:10 -0600",
 "tests/library_checker_aizu_tests/data_structures/simple_tree.test.cpp": "2024-12-14 15:47:13 -0600",
 "tests/library_checker_aizu_tests/data_structures/simple_tree_inc.test.cpp": "2024-12-21 00:23:10 -0500",
@@ -78,8 +78,8 @@
 "tests/library_checker_aizu_tests/handmade_tests/mobius.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/mod_int.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/n_choose_k.test.cpp": "2025-01-15 00:22:31 -0700",
-"tests/library_checker_aizu_tests/handmade_tests/permutation_tree_small.test.cpp": "2025-08-03 15:40:30 -0600",
-"tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp": "2025-08-03 15:40:30 -0600",
+"tests/library_checker_aizu_tests/handmade_tests/permutation_tree_small.test.cpp": "2025-08-03 17:30:02 -0600",
+"tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp": "2025-08-03 17:30:02 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/sa_find_subarray.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/seg_tree_find.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/seg_tree_find_small.test.cpp": "2024-12-14 19:50:29 -0600",
@@ -107,9 +107,9 @@
 "tests/library_checker_aizu_tests/math/xor_basis.test.cpp": "2025-04-22 21:37:22 -0500",
 "tests/library_checker_aizu_tests/math/xor_basis_intersection.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_binary_tree.test.cpp": "2025-02-10 14:50:36 -0700",
-"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_k_ary_tree.test.cpp": "2025-08-03 15:40:30 -0600",
-"tests/library_checker_aizu_tests/monotonic_stack_related/count_rectangles.test.cpp": "2025-08-03 15:40:30 -0600",
-"tests/library_checker_aizu_tests/monotonic_stack_related/max_rect_histogram.test.cpp": "2025-08-03 15:40:30 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_k_ary_tree.test.cpp": "2025-08-03 17:30:02 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/count_rectangles.test.cpp": "2025-08-03 17:30:02 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/max_rect_histogram.test.cpp": "2025-08-03 17:30:02 -0600",
 "tests/library_checker_aizu_tests/strings/kmp.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/strings/lcp_array.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/lcp_query_palindrome.test.cpp": "2025-02-10 14:50:36 -0700",
@@ -123,7 +123,7 @@
 "tests/library_checker_aizu_tests/strings/sa_cmp.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/sa_sort_pairs.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/single_matching_bs.test.cpp": "2025-02-10 14:50:36 -0700",
-"tests/library_checker_aizu_tests/strings/suffix_array.test.cpp": "2025-08-03 15:40:30 -0600",
+"tests/library_checker_aizu_tests/strings/suffix_array.test.cpp": "2025-08-03 17:30:02 -0600",
 "tests/library_checker_aizu_tests/strings/suffix_array_short.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/trie.test.cpp": "2024-12-05 10:41:42 -0600",
 "tests/library_checker_aizu_tests/strings/wildcard_pattern_matching.test.cpp": "2024-12-14 19:50:29 -0600",

From 312d08f26440353127d6a58882964b087c13bc09 Mon Sep 17 00:00:00 2001
From: Luke Videckis <lrvideckis@gmail.com>
Date: Sun, 3 Aug 2025 17:45:20 -0600
Subject: [PATCH 10/21] another style nit

---
 library/data_structures/uncommon/linear_rmq.hpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/library/data_structures/uncommon/linear_rmq.hpp b/library/data_structures/uncommon/linear_rmq.hpp
index 884bd532..e59f1ded 100644
--- a/library/data_structures/uncommon/linear_rmq.hpp
+++ b/library/data_structures/uncommon/linear_rmq.hpp
@@ -39,9 +39,9 @@ template<class T, class F> struct linear_rmq {
     if (unsigned j = in[l] ^ in[r]; j) {
       j = asc[l] & asc[r] & -bit_floor(j);
       if (unsigned k = asc[l] ^ j; k)
-        k = bit_floor(k), l = head[(in[l] & -k) | k];
+        k = bit_floor(k), l = head[-k & in[l] | k];
       if (unsigned k = asc[r] ^ j; k)
-        k = bit_floor(k), r = head[(in[r] & -k) | k];
+        k = bit_floor(k), r = head[-k & in[r] | k];
     }
     return cmp(a[l], a[r]) ? l : r;
   }

From dcfa30fe965e4425c5dda20fd908fa40db177c01 Mon Sep 17 00:00:00 2001
From: Luke Videckis <lrvideckis@gmail.com>
Date: Sun, 3 Aug 2025 17:58:03 -0600
Subject: [PATCH 11/21] another golf

---
 library/data_structures/uncommon/linear_rmq.hpp | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/library/data_structures/uncommon/linear_rmq.hpp b/library/data_structures/uncommon/linear_rmq.hpp
index e59f1ded..80ded2c6 100644
--- a/library/data_structures/uncommon/linear_rmq.hpp
+++ b/library/data_structures/uncommon/linear_rmq.hpp
@@ -20,16 +20,16 @@ template<class T, class F> struct linear_rmq {
     n(sz(a)), a(a), cmp(cmp), asc(n), in(n), head(n + 1) {
     vi st{-1};
     rep(i, 0, n + 1) {
-      int prev = -1;
+      int prev = 0;
       while (sz(st) > 1 &&
         (i == n || !cmp(a[st.back()], a[i]))) {
-        if (prev != -1) head[prev] = st.back();
+        if (prev) head[prev] = st.back();
         int b = bit_floor((end(st)[-2] + 1u) ^ i);
         in[st.back()] = prev = i & -b;
         st.pop_back();
         asc[st.back() + 1] |= b;
       }
-      if (prev != -1) head[prev] = i;
+      if (prev) head[prev] = i;
       st.push_back(i);
     }
     rep(i, 1, n)(asc[i] |= asc[i - 1]) &=

From c7f4999d1f14206785dde7e69c50db37a6105c89 Mon Sep 17 00:00:00 2001
From: Luke Videckis <lrvideckis@gmail.com>
Date: Sun, 3 Aug 2025 18:00:05 -0600
Subject: [PATCH 12/21] another golf

---
 library/data_structures/uncommon/linear_rmq.hpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/library/data_structures/uncommon/linear_rmq.hpp b/library/data_structures/uncommon/linear_rmq.hpp
index 80ded2c6..99f1c50e 100644
--- a/library/data_structures/uncommon/linear_rmq.hpp
+++ b/library/data_structures/uncommon/linear_rmq.hpp
@@ -23,13 +23,13 @@ template<class T, class F> struct linear_rmq {
       int prev = 0;
       while (sz(st) > 1 &&
         (i == n || !cmp(a[st.back()], a[i]))) {
-        if (prev) head[prev] = st.back();
+        head[prev] = st.back();
         int b = bit_floor((end(st)[-2] + 1u) ^ i);
         in[st.back()] = prev = i & -b;
         st.pop_back();
         asc[st.back() + 1] |= b;
       }
-      if (prev) head[prev] = i;
+      head[prev] = i;
       st.push_back(i);
     }
     rep(i, 1, n)(asc[i] |= asc[i - 1]) &=

From e874bccd3213a249700e99e219659da9e3b52262 Mon Sep 17 00:00:00 2001
From: GitHub <noreply@github.com>
Date: Mon, 4 Aug 2025 00:13:44 +0000
Subject: [PATCH 13/21] [auto-verifier] verify commit
 c7f4999d1f14206785dde7e69c50db37a6105c89

---
 .verify-helper/timestamps.remote.json | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/.verify-helper/timestamps.remote.json b/.verify-helper/timestamps.remote.json
index b63e01f6..a5bc1ba8 100644
--- a/.verify-helper/timestamps.remote.json
+++ b/.verify-helper/timestamps.remote.json
@@ -33,15 +33,15 @@
 "tests/library_checker_aizu_tests/data_structures/line_tree_lib_checker.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/data_structures/merge_sort_tree.test.cpp": "2025-02-11 13:53:30 -0700",
 "tests/library_checker_aizu_tests/data_structures/mode_query.test.cpp": "2025-02-10 23:30:47 -0700",
-"tests/library_checker_aizu_tests/data_structures/permutation_tree.test.cpp": "2025-08-03 17:30:02 -0600",
+"tests/library_checker_aizu_tests/data_structures/permutation_tree.test.cpp": "2025-08-03 18:00:05 -0600",
 "tests/library_checker_aizu_tests/data_structures/persistent_queue_tree.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/persistent_seg_tree.test.cpp": "2024-12-05 10:41:42 -0600",
 "tests/library_checker_aizu_tests/data_structures/pq_ds_undo_sliding_window.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/pq_ds_undo_with_dsu.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/range_parallel_dsu.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/data_structures/rmq_disjoint_sparse_table.test.cpp": "2024-12-15 14:34:10 -0600",
-"tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp": "2025-08-03 17:30:02 -0600",
-"tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2025-08-03 17:30:02 -0600",
+"tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp": "2025-08-03 18:00:05 -0600",
+"tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2025-08-03 18:00:05 -0600",
 "tests/library_checker_aizu_tests/data_structures/rmq_sparse_table_inc.test.cpp": "2024-12-15 14:34:10 -0600",
 "tests/library_checker_aizu_tests/data_structures/simple_tree.test.cpp": "2024-12-14 15:47:13 -0600",
 "tests/library_checker_aizu_tests/data_structures/simple_tree_inc.test.cpp": "2024-12-21 00:23:10 -0500",
@@ -78,8 +78,8 @@
 "tests/library_checker_aizu_tests/handmade_tests/mobius.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/mod_int.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/n_choose_k.test.cpp": "2025-01-15 00:22:31 -0700",
-"tests/library_checker_aizu_tests/handmade_tests/permutation_tree_small.test.cpp": "2025-08-03 17:30:02 -0600",
-"tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp": "2025-08-03 17:30:02 -0600",
+"tests/library_checker_aizu_tests/handmade_tests/permutation_tree_small.test.cpp": "2025-08-03 18:00:05 -0600",
+"tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp": "2025-08-03 18:00:05 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/sa_find_subarray.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/seg_tree_find.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/seg_tree_find_small.test.cpp": "2024-12-14 19:50:29 -0600",
@@ -107,9 +107,9 @@
 "tests/library_checker_aizu_tests/math/xor_basis.test.cpp": "2025-04-22 21:37:22 -0500",
 "tests/library_checker_aizu_tests/math/xor_basis_intersection.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_binary_tree.test.cpp": "2025-02-10 14:50:36 -0700",
-"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_k_ary_tree.test.cpp": "2025-08-03 17:30:02 -0600",
-"tests/library_checker_aizu_tests/monotonic_stack_related/count_rectangles.test.cpp": "2025-08-03 17:30:02 -0600",
-"tests/library_checker_aizu_tests/monotonic_stack_related/max_rect_histogram.test.cpp": "2025-08-03 17:30:02 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_k_ary_tree.test.cpp": "2025-08-03 18:00:05 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/count_rectangles.test.cpp": "2025-08-03 18:00:05 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/max_rect_histogram.test.cpp": "2025-08-03 18:00:05 -0600",
 "tests/library_checker_aizu_tests/strings/kmp.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/strings/lcp_array.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/lcp_query_palindrome.test.cpp": "2025-02-10 14:50:36 -0700",
@@ -123,7 +123,7 @@
 "tests/library_checker_aizu_tests/strings/sa_cmp.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/sa_sort_pairs.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/single_matching_bs.test.cpp": "2025-02-10 14:50:36 -0700",
-"tests/library_checker_aizu_tests/strings/suffix_array.test.cpp": "2025-08-03 17:30:02 -0600",
+"tests/library_checker_aizu_tests/strings/suffix_array.test.cpp": "2025-08-03 18:00:05 -0600",
 "tests/library_checker_aizu_tests/strings/suffix_array_short.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/trie.test.cpp": "2024-12-05 10:41:42 -0600",
 "tests/library_checker_aizu_tests/strings/wildcard_pattern_matching.test.cpp": "2024-12-14 19:50:29 -0600",

From 321f46d35cb371b03a3bc79997e5b3ebb0700024 Mon Sep 17 00:00:00 2001
From: Luke Videckis <lrvideckis@gmail.com>
Date: Sun, 3 Aug 2025 18:14:28 -0600
Subject: [PATCH 14/21] will hopefully fix the warning

---
 library/data_structures/uncommon/linear_rmq.hpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/library/data_structures/uncommon/linear_rmq.hpp b/library/data_structures/uncommon/linear_rmq.hpp
index 99f1c50e..bb7ffd05 100644
--- a/library/data_structures/uncommon/linear_rmq.hpp
+++ b/library/data_structures/uncommon/linear_rmq.hpp
@@ -39,9 +39,9 @@ template<class T, class F> struct linear_rmq {
     if (unsigned j = in[l] ^ in[r]; j) {
       j = asc[l] & asc[r] & -bit_floor(j);
       if (unsigned k = asc[l] ^ j; k)
-        k = bit_floor(k), l = head[-k & in[l] | k];
+        k = bit_floor(k), l = head[k | in[l] & -k];
       if (unsigned k = asc[r] ^ j; k)
-        k = bit_floor(k), r = head[-k & in[r] | k];
+        k = bit_floor(k), r = head[k | in[r] & -k];
     }
     return cmp(a[l], a[r]) ? l : r;
   }

From 822e46ae60c7783dcb402394c873945ef9cdad6a Mon Sep 17 00:00:00 2001
From: Luke Videckis <lrvideckis@gmail.com>
Date: Sun, 3 Aug 2025 18:17:06 -0600
Subject: [PATCH 15/21] revert to fix warning

---
 library/data_structures/uncommon/linear_rmq.hpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/library/data_structures/uncommon/linear_rmq.hpp b/library/data_structures/uncommon/linear_rmq.hpp
index bb7ffd05..072015f6 100644
--- a/library/data_structures/uncommon/linear_rmq.hpp
+++ b/library/data_structures/uncommon/linear_rmq.hpp
@@ -39,9 +39,9 @@ template<class T, class F> struct linear_rmq {
     if (unsigned j = in[l] ^ in[r]; j) {
       j = asc[l] & asc[r] & -bit_floor(j);
       if (unsigned k = asc[l] ^ j; k)
-        k = bit_floor(k), l = head[k | in[l] & -k];
+        k = bit_floor(k), l = head[(in[l] & -k) | k];
       if (unsigned k = asc[r] ^ j; k)
-        k = bit_floor(k), r = head[k | in[r] & -k];
+        k = bit_floor(k), r = head[(in[r] & -k) | k];
     }
     return cmp(a[l], a[r]) ? l : r;
   }

From e41d2e35ae31296eaa9b6a13a6bc0d204a225909 Mon Sep 17 00:00:00 2001
From: GitHub <noreply@github.com>
Date: Mon, 4 Aug 2025 00:31:09 +0000
Subject: [PATCH 16/21] [auto-verifier] verify commit
 822e46ae60c7783dcb402394c873945ef9cdad6a

---
 .verify-helper/timestamps.remote.json | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/.verify-helper/timestamps.remote.json b/.verify-helper/timestamps.remote.json
index a5bc1ba8..e9b3d3c2 100644
--- a/.verify-helper/timestamps.remote.json
+++ b/.verify-helper/timestamps.remote.json
@@ -33,15 +33,15 @@
 "tests/library_checker_aizu_tests/data_structures/line_tree_lib_checker.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/data_structures/merge_sort_tree.test.cpp": "2025-02-11 13:53:30 -0700",
 "tests/library_checker_aizu_tests/data_structures/mode_query.test.cpp": "2025-02-10 23:30:47 -0700",
-"tests/library_checker_aizu_tests/data_structures/permutation_tree.test.cpp": "2025-08-03 18:00:05 -0600",
+"tests/library_checker_aizu_tests/data_structures/permutation_tree.test.cpp": "2025-08-03 18:17:06 -0600",
 "tests/library_checker_aizu_tests/data_structures/persistent_queue_tree.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/persistent_seg_tree.test.cpp": "2024-12-05 10:41:42 -0600",
 "tests/library_checker_aizu_tests/data_structures/pq_ds_undo_sliding_window.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/pq_ds_undo_with_dsu.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/range_parallel_dsu.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/data_structures/rmq_disjoint_sparse_table.test.cpp": "2024-12-15 14:34:10 -0600",
-"tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp": "2025-08-03 18:00:05 -0600",
-"tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2025-08-03 18:00:05 -0600",
+"tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp": "2025-08-03 18:17:06 -0600",
+"tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2025-08-03 18:17:06 -0600",
 "tests/library_checker_aizu_tests/data_structures/rmq_sparse_table_inc.test.cpp": "2024-12-15 14:34:10 -0600",
 "tests/library_checker_aizu_tests/data_structures/simple_tree.test.cpp": "2024-12-14 15:47:13 -0600",
 "tests/library_checker_aizu_tests/data_structures/simple_tree_inc.test.cpp": "2024-12-21 00:23:10 -0500",
@@ -78,8 +78,8 @@
 "tests/library_checker_aizu_tests/handmade_tests/mobius.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/mod_int.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/n_choose_k.test.cpp": "2025-01-15 00:22:31 -0700",
-"tests/library_checker_aizu_tests/handmade_tests/permutation_tree_small.test.cpp": "2025-08-03 18:00:05 -0600",
-"tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp": "2025-08-03 18:00:05 -0600",
+"tests/library_checker_aizu_tests/handmade_tests/permutation_tree_small.test.cpp": "2025-08-03 18:17:06 -0600",
+"tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp": "2025-08-03 18:17:06 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/sa_find_subarray.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/seg_tree_find.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/seg_tree_find_small.test.cpp": "2024-12-14 19:50:29 -0600",
@@ -107,9 +107,9 @@
 "tests/library_checker_aizu_tests/math/xor_basis.test.cpp": "2025-04-22 21:37:22 -0500",
 "tests/library_checker_aizu_tests/math/xor_basis_intersection.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_binary_tree.test.cpp": "2025-02-10 14:50:36 -0700",
-"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_k_ary_tree.test.cpp": "2025-08-03 18:00:05 -0600",
-"tests/library_checker_aizu_tests/monotonic_stack_related/count_rectangles.test.cpp": "2025-08-03 18:00:05 -0600",
-"tests/library_checker_aizu_tests/monotonic_stack_related/max_rect_histogram.test.cpp": "2025-08-03 18:00:05 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_k_ary_tree.test.cpp": "2025-08-03 18:17:06 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/count_rectangles.test.cpp": "2025-08-03 18:17:06 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/max_rect_histogram.test.cpp": "2025-08-03 18:17:06 -0600",
 "tests/library_checker_aizu_tests/strings/kmp.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/strings/lcp_array.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/lcp_query_palindrome.test.cpp": "2025-02-10 14:50:36 -0700",
@@ -123,7 +123,7 @@
 "tests/library_checker_aizu_tests/strings/sa_cmp.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/sa_sort_pairs.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/single_matching_bs.test.cpp": "2025-02-10 14:50:36 -0700",
-"tests/library_checker_aizu_tests/strings/suffix_array.test.cpp": "2025-08-03 18:00:05 -0600",
+"tests/library_checker_aizu_tests/strings/suffix_array.test.cpp": "2025-08-03 18:17:06 -0600",
 "tests/library_checker_aizu_tests/strings/suffix_array_short.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/trie.test.cpp": "2024-12-05 10:41:42 -0600",
 "tests/library_checker_aizu_tests/strings/wildcard_pattern_matching.test.cpp": "2024-12-14 19:50:29 -0600",

From 4d6a02b5d44f50599d63a6261a4968fa9cdefd43 Mon Sep 17 00:00:00 2001
From: Luke Videckis <lrvideckis@gmail.com>
Date: Sun, 3 Aug 2025 18:39:58 -0600
Subject: [PATCH 17/21] nit

---
 library/data_structures/uncommon/linear_rmq.hpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/library/data_structures/uncommon/linear_rmq.hpp b/library/data_structures/uncommon/linear_rmq.hpp
index 072015f6..0847d3d2 100644
--- a/library/data_structures/uncommon/linear_rmq.hpp
+++ b/library/data_structures/uncommon/linear_rmq.hpp
@@ -15,9 +15,9 @@ template<class T, class F> struct linear_rmq {
   int n;
   vector<T> a;
   F cmp;
-  vi asc, in, head;
+  vi in, asc, head;
   linear_rmq(const vector<T>& a, F cmp):
-    n(sz(a)), a(a), cmp(cmp), asc(n), in(n), head(n + 1) {
+    n(sz(a)), a(a), cmp(cmp), in(n), asc(n), head(n + 1) {
     vi st{-1};
     rep(i, 0, n + 1) {
       int prev = 0;

From 7d255ba4edb1aac4c028960c8c64bbc30db8923b Mon Sep 17 00:00:00 2001
From: GitHub <noreply@github.com>
Date: Mon, 4 Aug 2025 00:53:26 +0000
Subject: [PATCH 18/21] [auto-verifier] verify commit
 4d6a02b5d44f50599d63a6261a4968fa9cdefd43

---
 .verify-helper/timestamps.remote.json | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/.verify-helper/timestamps.remote.json b/.verify-helper/timestamps.remote.json
index e9b3d3c2..b889bacf 100644
--- a/.verify-helper/timestamps.remote.json
+++ b/.verify-helper/timestamps.remote.json
@@ -33,15 +33,15 @@
 "tests/library_checker_aizu_tests/data_structures/line_tree_lib_checker.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/data_structures/merge_sort_tree.test.cpp": "2025-02-11 13:53:30 -0700",
 "tests/library_checker_aizu_tests/data_structures/mode_query.test.cpp": "2025-02-10 23:30:47 -0700",
-"tests/library_checker_aizu_tests/data_structures/permutation_tree.test.cpp": "2025-08-03 18:17:06 -0600",
+"tests/library_checker_aizu_tests/data_structures/permutation_tree.test.cpp": "2025-08-03 18:39:58 -0600",
 "tests/library_checker_aizu_tests/data_structures/persistent_queue_tree.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/persistent_seg_tree.test.cpp": "2024-12-05 10:41:42 -0600",
 "tests/library_checker_aizu_tests/data_structures/pq_ds_undo_sliding_window.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/pq_ds_undo_with_dsu.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/data_structures/range_parallel_dsu.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/data_structures/rmq_disjoint_sparse_table.test.cpp": "2024-12-15 14:34:10 -0600",
-"tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp": "2025-08-03 18:17:06 -0600",
-"tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2025-08-03 18:17:06 -0600",
+"tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp": "2025-08-03 18:39:58 -0600",
+"tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2025-08-03 18:39:58 -0600",
 "tests/library_checker_aizu_tests/data_structures/rmq_sparse_table_inc.test.cpp": "2024-12-15 14:34:10 -0600",
 "tests/library_checker_aizu_tests/data_structures/simple_tree.test.cpp": "2024-12-14 15:47:13 -0600",
 "tests/library_checker_aizu_tests/data_structures/simple_tree_inc.test.cpp": "2024-12-21 00:23:10 -0500",
@@ -78,8 +78,8 @@
 "tests/library_checker_aizu_tests/handmade_tests/mobius.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/mod_int.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/n_choose_k.test.cpp": "2025-01-15 00:22:31 -0700",
-"tests/library_checker_aizu_tests/handmade_tests/permutation_tree_small.test.cpp": "2025-08-03 18:17:06 -0600",
-"tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp": "2025-08-03 18:17:06 -0600",
+"tests/library_checker_aizu_tests/handmade_tests/permutation_tree_small.test.cpp": "2025-08-03 18:39:58 -0600",
+"tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp": "2025-08-03 18:39:58 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/sa_find_subarray.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/seg_tree_find.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/seg_tree_find_small.test.cpp": "2024-12-14 19:50:29 -0600",
@@ -107,9 +107,9 @@
 "tests/library_checker_aizu_tests/math/xor_basis.test.cpp": "2025-04-22 21:37:22 -0500",
 "tests/library_checker_aizu_tests/math/xor_basis_intersection.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_binary_tree.test.cpp": "2025-02-10 14:50:36 -0700",
-"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_k_ary_tree.test.cpp": "2025-08-03 18:17:06 -0600",
-"tests/library_checker_aizu_tests/monotonic_stack_related/count_rectangles.test.cpp": "2025-08-03 18:17:06 -0600",
-"tests/library_checker_aizu_tests/monotonic_stack_related/max_rect_histogram.test.cpp": "2025-08-03 18:17:06 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_k_ary_tree.test.cpp": "2025-08-03 18:39:58 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/count_rectangles.test.cpp": "2025-08-03 18:39:58 -0600",
+"tests/library_checker_aizu_tests/monotonic_stack_related/max_rect_histogram.test.cpp": "2025-08-03 18:39:58 -0600",
 "tests/library_checker_aizu_tests/strings/kmp.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/strings/lcp_array.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/lcp_query_palindrome.test.cpp": "2025-02-10 14:50:36 -0700",
@@ -123,7 +123,7 @@
 "tests/library_checker_aizu_tests/strings/sa_cmp.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/sa_sort_pairs.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/single_matching_bs.test.cpp": "2025-02-10 14:50:36 -0700",
-"tests/library_checker_aizu_tests/strings/suffix_array.test.cpp": "2025-08-03 18:17:06 -0600",
+"tests/library_checker_aizu_tests/strings/suffix_array.test.cpp": "2025-08-03 18:39:58 -0600",
 "tests/library_checker_aizu_tests/strings/suffix_array_short.test.cpp": "2025-02-10 14:50:36 -0700",
 "tests/library_checker_aizu_tests/strings/trie.test.cpp": "2024-12-05 10:41:42 -0600",
 "tests/library_checker_aizu_tests/strings/wildcard_pattern_matching.test.cpp": "2024-12-14 19:50:29 -0600",

From 0084dcf62bd2141e9b6a153587e099470f667428 Mon Sep 17 00:00:00 2001
From: Luke Videckis <lrvideckis@gmail.com>
Date: Sun, 3 Aug 2025 19:00:12 -0600
Subject: [PATCH 19/21] I like this way

---
 library/data_structures/uncommon/linear_rmq.hpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/library/data_structures/uncommon/linear_rmq.hpp b/library/data_structures/uncommon/linear_rmq.hpp
index 0847d3d2..8aca5af9 100644
--- a/library/data_structures/uncommon/linear_rmq.hpp
+++ b/library/data_structures/uncommon/linear_rmq.hpp
@@ -32,8 +32,8 @@ template<class T, class F> struct linear_rmq {
       head[prev] = i;
       st.push_back(i);
     }
-    rep(i, 1, n)(asc[i] |= asc[i - 1]) &=
-      -(in[i] & -in[i]);
+    rep(i, 1, n) asc[i] =
+      (asc[i] | asc[i - 1]) & -(in[i] & -in[i]);
   }
   int idx(int l, int r) { // [l, r]
     if (unsigned j = in[l] ^ in[r]; j) {

From 780363b543d963f94e5d45465ced8df8132734ae Mon Sep 17 00:00:00 2001
From: Luke Videckis <lrvideckis@gmail.com>
Date: Sun, 3 Aug 2025 19:02:48 -0600
Subject: [PATCH 20/21] more golf

---
 library/data_structures/uncommon/linear_rmq.hpp | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/library/data_structures/uncommon/linear_rmq.hpp b/library/data_structures/uncommon/linear_rmq.hpp
index 8aca5af9..ab5314f2 100644
--- a/library/data_structures/uncommon/linear_rmq.hpp
+++ b/library/data_structures/uncommon/linear_rmq.hpp
@@ -24,13 +24,12 @@ template<class T, class F> struct linear_rmq {
       while (sz(st) > 1 &&
         (i == n || !cmp(a[st.back()], a[i]))) {
         head[prev] = st.back();
-        int b = bit_floor((end(st)[-2] + 1u) ^ i);
+        auto k = end(st)[-2] + 1u, b = bit_floor(k ^ i);
         in[st.back()] = prev = i & -b;
+        asc[k] |= b;
         st.pop_back();
-        asc[st.back() + 1] |= b;
       }
-      head[prev] = i;
-      st.push_back(i);
+      st.push_back(head[prev] = i);
     }
     rep(i, 1, n) asc[i] =
       (asc[i] | asc[i - 1]) & -(in[i] & -in[i]);

From 9717342c17cee967eba4e89ff7ba5a53d6c2705d Mon Sep 17 00:00:00 2001
From: Luke Videckis <lrvideckis@gmail.com>
Date: Sun, 3 Aug 2025 19:03:21 -0600
Subject: [PATCH 21/21] more golf

---
 library/data_structures/uncommon/linear_rmq.hpp | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/library/data_structures/uncommon/linear_rmq.hpp b/library/data_structures/uncommon/linear_rmq.hpp
index ab5314f2..d7f05ea3 100644
--- a/library/data_structures/uncommon/linear_rmq.hpp
+++ b/library/data_structures/uncommon/linear_rmq.hpp
@@ -25,8 +25,7 @@ template<class T, class F> struct linear_rmq {
         (i == n || !cmp(a[st.back()], a[i]))) {
         head[prev] = st.back();
         auto k = end(st)[-2] + 1u, b = bit_floor(k ^ i);
-        in[st.back()] = prev = i & -b;
-        asc[k] |= b;
+        in[st.back()] = prev = i & -b, asc[k] |= b;
         st.pop_back();
       }
       st.push_back(head[prev] = i);