#include <bits/stdc++.h>
#include "bubblesort2.h"
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define MASK(i) (1LL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
#define block_of_code if(true)
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll gcd(ll a, ll b){return __gcd(a, b);}
ll lcm(ll a, ll b){return a / gcd(a, b) * b;}
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ll mask){return __builtin_popcountll(mask);}
int ctz(ull mask){return __builtin_ctzll(mask);}
int logOf(ull mask){return 63 - __builtin_clzll(mask);}
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
ll rngesus(ll l, ll r){return l + (ull) rng() % (r - l + 1);}
double rngesus_d(double l, double r){
double cur = rngesus(0, MASK(60) - 1);
cur /= MASK(60) - 1;
return l + cur * (r - l);
}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T container, string separator = " ", string finish = "\n", ostream &out = cout){
for(auto item: container) out << item << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
const int BLOCK = 3000;
int di(int x, int y){
return x / y + (x % y > 0);
}
struct SegmentTree{
int n;
vector<int> a, lazy;
SegmentTree(int _n){
n = _n;
a.resize(n * 4 + 4); lazy.resize(n * 4 + 4);
}
void update_node(int i, int v){
a[i] += v;
lazy[i] += v;
}
void down(int id){
update_node(id * 2, lazy[id]); update_node(id * 2 + 1, lazy[id]);
lazy[id] = 0;
}
void update(int u, int v, int val){if (u <= v) update(u, v, val, 0, n-1, 1);}
void update(int u, int v, int val, int l, int r, int id){
if (u <= l && r <= v){
update_node(id, val);
return;
}
if (lazy[id]) down(id);
int mid = (l + r) >> 1;
if (u <= mid) update(u, v, val, l, mid, id * 2);
if (v > mid) update(u, v, val, mid + 1, r, id * 2 + 1);
a[id] = max(a[id * 2], a[id * 2 + 1]);
}
int get(){return a[1];}
void build_tree(vector<int> b){build_tree(b, 0, n-1, 1);}
void build_tree(vector<int> &b, int l, int r, int id){
if (l == r){a[id] = b[l]; return;}
lazy[id] = 0;
int mid = (l + r) >> 1;
build_tree(b, l, mid, id * 2); build_tree(b, mid + 1, r, id * 2 + 1);
a[id] = max(a[id * 2], a[id * 2 + 1]);
}
vector<int> get_tree(){
vector<int> ans(n);
get_tree(ans, 0, n-1, 1);
return ans;
}
void get_tree(vector<int> &ans, int l, int r, int id){
if (l == r){ans[l] = a[id]; return;}
if (lazy[id]) down(id);
int mid = (l + r) >> 1;
get_tree(ans, l, mid, id * 2); get_tree(ans, mid + 1, r, id * 2 + 1);
}
};
vector<int> countScans(vector<int> a,vector<int> X,vector<int> V){
int n = a.size(), q = X.size();
int b_n = di(n, BLOCK);
vector<vector<pair<int, int>>> stair(b_n);
vector<SegmentTree> sigma;
for(int i = 0; i < n; ++i){
stair[i / BLOCK].push_back({a[i],i});
}
for(int i = 0; i < b_n; ++i) sort(ALL(stair[i]));
for(int i = 0; i < b_n; ++i){
sigma.push_back(SegmentTree(stair[i].size()));
for(int k = 0; k < stair[i].size(); ++k){
int cur = 0;
for(int j = 0; j < i; ++j){
int idx = upper_bound(ALL(stair[j]), stair[i][k]) - stair[j].begin();
cur += stair[j].size() - idx;
}
for(int j = k + 1; j < stair[i].size(); ++j) if (stair[i][j].second < stair[i][k].second)
cur++;
sigma[i].update(k, k, cur);
}
}
vector<int> answer(q);
for(int cur_query = 0; cur_query < q; ++cur_query){
// cout << "Query: " << cur_query << endl;
int u = X[cur_query], v = V[cur_query];
int cur_b = u / BLOCK;
for(int i = cur_b + 1; i < b_n; ++i){
int idx = lower_bound(ALL(stair[i]), make_pair(a[u], -1)) - stair[i].begin() - 1;
sigma[i].update(0, idx, -1);
idx = lower_bound(ALL(stair[i]), make_pair(v, -1)) - stair[i].begin() - 1;
sigma[i].update(0, idx, 1);
}
int idx = lower_bound(ALL(stair[cur_b]), make_pair(a[u], u)) - stair[cur_b].begin();
vector<int> cur_sigma = sigma[cur_b].get_tree();
a[u] = v;
stair[cur_b][idx] = make_pair(a[u], u);
while (idx + 1 < stair[cur_b].size() && stair[cur_b][idx] > stair[cur_b][idx + 1]){
if (stair[cur_b][idx].second < stair[cur_b][idx + 1].second) cur_sigma[idx + 1]++;
swap(stair[cur_b][idx], stair[cur_b][idx + 1]);
swap(cur_sigma[idx], cur_sigma[idx + 1]);
idx++;
}
while (idx > 0 && stair[cur_b][idx - 1] > stair[cur_b][idx]){
if (stair[cur_b][idx].second < stair[cur_b][idx - 1].second) cur_sigma[idx - 1]--;
swap(stair[cur_b][idx], stair[cur_b][idx - 1]);
swap(cur_sigma[idx], cur_sigma[idx - 1]);
idx--;
}
cur_sigma[idx] = 0;
for(int j = 0; j < cur_b; ++j){
int _idx = upper_bound(ALL(stair[j]), stair[cur_b][idx]) - stair[j].begin();
cur_sigma[idx] += stair[j].size() - _idx;
}
for(int j = idx + 1; j < stair[cur_b].size(); ++j) if (stair[cur_b][j].second < stair[cur_b][idx].second)
cur_sigma[idx]++;
sigma[cur_b].build_tree(cur_sigma);
int ans = 0;
for(int i = 0; i < b_n; ++i) maximize(ans, sigma[i].get());
answer[cur_query] = ans;
// for(int i = 0; i<b_n; ++i){
// vector<int> sig = sigma[i].get_tree();
// printArr(sig, " ", "");
// }
// cout << "\n";
}
return answer;
}
// int main(void){
// ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
// int n, q; cin >> n >> q;
// vector<int> a(n);
// for(int i = 0; i<n; ++i) cin >> a[i];
// vector<int> x(q), v(q);
// for(int i = 0; i<q; ++i) cin >> x[i] >> v[i];
// printArr(countScans(a, x, v));
// return 0;
// }
