// Om Namah Shivaya
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x, y) ((x + y - 1) / (y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i, n) for(int i = 0; i < n; ++i)
#define rep1(i, n) for(int i = 1; i <= n; ++i)
#define rev(i, s, e) for(int i = s; i >= e; --i)
#define trav(i, a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a, b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a, b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
refs:
edi: http://s3-ap-northeast-1.amazonaws.com/data.cms.ioi-jp.org/open-2018/2018-open-bubblesort2-sol-en.pdf
https://codeforces.com/blog/entry/61340?#comment-452982
(read edi of linked usaco problem, it contains the proof for the approach mentioned in the joi edi)
*/
#include "bubblesort2.h"
const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
template<typename T>
struct fenwick {
int siz;
vector<T> tree;
fenwick(int n) {
siz = n;
tree = vector<T>(n + 1);
}
int lsb(int x) {
return x & -x;
}
void build(vector<T> &a, int n) {
for (int i = 1; i <= n; ++i) {
int par = i + lsb(i);
tree[i] += a[i];
if (par <= siz) {
tree[par] += tree[i];
}
}
}
void pupd(int i, T v) {
i++;
while (i <= siz) {
tree[i] += v;
i += lsb(i);
}
}
T sum(int i) {
i++;
T res = 0;
while (i) {
res += tree[i];
i -= lsb(i);
}
return res;
}
T query(int l, int r) {
if (l > r) return 0;
T res = sum(r) - sum(l - 1);
return res;
}
};
template<typename T>
struct lazysegtree {
/*=======================================================*/
struct data {
int a;
};
struct lazy {
int a;
};
data d_neutral = { -inf1};
lazy l_neutral = {0};
void merge(data &curr, data &left, data &right) {
curr.a = max(left.a, right.a);
}
void create(int x, int lx, int rx, T v) {
tr[x].a = v;
}
void modify(int x, int lx, int rx, T v) {
if (v.ff == 1) {
// set
tr[x].a = v.ss;
}
else {
// add
lz[x].a = v.ss;
}
}
void propagate(int x, int lx, int rx) {
ll v = lz[x].a;
if (!v) return;
tr[x].a += v;
if (rx - lx > 1) {
lz[2 * x + 1].a += v;
lz[2 * x + 2].a += v;
}
lz[x] = l_neutral;
}
/*=======================================================*/
int siz = 1;
vector<data> tr;
vector<lazy> lz;
lazysegtree() {
}
lazysegtree(int n) {
while (siz < n) siz *= 2;
tr.assign(2 * siz, d_neutral);
lz.assign(2 * siz, l_neutral);
}
void build(vector<T> &a, int n, int x, int lx, int rx) {
if (rx - lx == 1) {
if (lx < n) {
create(x, lx, rx, a[lx]);
}
return;
}
int mid = (lx + rx) / 2;
build(a, n, 2 * x + 1, lx, mid);
build(a, n, 2 * x + 2, mid, rx);
merge(tr[x], tr[2 * x + 1], tr[2 * x + 2]);
}
void build(vector<T> &a, int n) {
build(a, n, 0, 0, siz);
}
void rupd(int l, int r, T v, int x, int lx, int rx) {
propagate(x, lx, rx);
if (lx >= r or rx <= l) return;
if (lx >= l and rx <= r) {
modify(x, lx, rx, v);
propagate(x, lx, rx);
return;
}
int mid = (lx + rx) / 2;
rupd(l, r, v, 2 * x + 1, lx, mid);
rupd(l, r, v, 2 * x + 2, mid, rx);
merge(tr[x], tr[2 * x + 1], tr[2 * x + 2]);
}
void rupd(int l, int r, T v) {
rupd(l, r + 1, v, 0, 0, siz);
}
data query(int l, int r, int x, int lx, int rx) {
propagate(x, lx, rx);
if (lx >= r or rx <= l) return d_neutral;
if (lx >= l and rx <= r) return tr[x];
int mid = (lx + rx) / 2;
data curr;
data left = query(l, r, 2 * x + 1, lx, mid);
data right = query(l, r, 2 * x + 2, mid, rx);
merge(curr, left, right);
return curr;
}
data query(int l, int r) {
return query(l, r + 1, 0, 0, siz);
}
};
vector<int> countScans(vector<int> a, vector<int> qx, vector<int> qv) {
int n = sz(a);
int q = sz(qx);
vector<pii> b;
rep(i, n) {
b.pb({a[i], i});
}
rep(i, q) {
b.pb({qv[i], qx[i]});
}
sort(all(b));
b.resize(unique(all(b)) - b.begin());
int siz = sz(b);
auto get_ind = [&](pii p) {
return lower_bound(all(b), p) - b.begin();
};
lazysegtree<pii> st(siz + 5);
fenwick<int> fenw(siz + 5);
rep(i, n) {
int ind = get_ind({a[i], i});
st.rupd(ind, ind, {1, i});
fenw.pupd(ind, 1);
}
rep(i, n) {
int ind = get_ind({a[i], i});
st.rupd(ind + 1, siz, {2, -1});
}
vector<int> ans(q);
rep(id, q) {
int i = qx[id];
int v = qv[id];
int ind1 = get_ind({a[i], i});
st.rupd(ind1, ind1, {1, -inf1});
st.rupd(ind1, siz, {2, 1});
fenw.pupd(ind1, -1);
a[i] = v;
int ind2 = get_ind({a[i], i});
int smaller = fenw.query(0, ind2 - 1);
st.rupd(ind2, ind2, {1, i - smaller});
st.rupd(ind2 + 1, siz, {2, -1});
fenw.pupd(ind2, 1);
ans[id] = st.query(0, siz).a;
}
return ans;
}
