#include <bits/stdc++.h>
using namespace std ;
#define int int64_t //be careful about this
#define endl "\n"
#define f(i,a,b) for(int i=int(a);i<int(b);++i)
#define pr pair
#define ar array
#define fr first
#define sc second
#define vt vector
#define pb push_back
#define eb emplace_back
#define LB lower_bound
#define UB upper_bound
#define PQ priority_queue
#define sz(x) ((int)(x).size())
#define all(a) (a).begin(),(a).end()
#define allr(a) (a).rbegin(),(a).rend()
#define mem0(a) memset(a, 0, sizeof(a))
#define mem1(a) memset(a, -1, sizeof(a))
template<class A> void rd(vt<A>& v);
template<class T> void rd(T& x){ cin >> x; }
template<class H, class... T> void rd(H& h, T&... t) { rd(h) ; rd(t...) ;}
template<class A> void rd(vt<A>& x) { for(auto& a : x) rd(a) ;}
template<class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
template<typename T>
void __p(T a) {
cout<<a;
}
template<typename T, typename F>
void __p(pair<T, F> a) {
cout<<"{";
__p(a.first);
cout<<",";
__p(a.second);
cout<<"}\n";
}
template<typename T>
void __p(std::vector<T> a) {
cout<<"{";
for(auto it=a.begin(); it<a.end(); it++)
__p(*it),cout<<",}\n"[it+1==a.end()];
}
template<typename T, typename ...Arg>
void __p(T a1, Arg ...a) {
__p(a1);
__p(a...);
}
template<typename Arg1>
void __f(const char *name, Arg1 &&arg1) {
cout<<name<<" : ";
__p(arg1);
cout<<endl;
}
template<typename Arg1, typename ... Args>
void __f(const char *names, Arg1 &&arg1, Args &&... args) {
int bracket=0,i=0;
for(;; i++)
if(names[i]==','&&bracket==0)
break;
else if(names[i]=='(')
bracket++;
else if(names[i]==')')
bracket--;
const char *comma=names+i;
cout.write(names,comma-names)<<" : ";
__p(arg1);
cout<<" | ";
__f(comma+1,args...);
}
void setIO(string s = "") {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
cin.exceptions(cin.failbit);
cout.precision(15); cout << fixed;
#ifdef ONLINE_JUDGE
if(sz(s)){
freopen((s+".in").c_str(),"r",stdin);
freopen((s+".out").c_str(),"w",stdout);
}
#define __f(...) 0
#endif
}
/*
* Description segment tree for mass changes using lazy propagation
* source: pashka edu course with very little own modifications
* verify commutivity and distributivity property for changes, assignement ans sum do not follow these property
* set ID, NEUTRAL_ELEMENT, NO_OPERATION accordingly.
* update on interval [l, r) and query val at range [l, r)
* change x tells that at x this change is done but have to propogate to children
* verification :- https://codeforces.com/edu/course/2/lesson/5/2/practice/status
*/
const int inf = 1e9;
template<class T, class H> struct lazy_segment_tree {
const T ID = 0, NEUTRAL_ELEMENT = 0;
const H NO_OPERATION = 0;
int size ;
vector<T> segment_tree;
vector<H> change;
void apply_lazy_on_change(H &a, H b){
a += b;
}
T combiner_function(T a, T b){
return max(a,b);
}
void apply_lazy_on_node(T &a, H b){
a += b;
}
void propogate(int x, int lx, int rx){
if(rx - lx == 1) return ;
apply_lazy_on_node(segment_tree[2 * x + 1], change[x]);
apply_lazy_on_node(segment_tree[2 * x + 2], change[x]);
apply_lazy_on_change(change[2 * x + 1], change[x]);
apply_lazy_on_change(change[2 * x + 2], change[x]);
change[x] = NO_OPERATION;
}
void init(int n){
size = 1;
while(size < n) size *= 2;
segment_tree.assign(2*size - 1, ID);
change.assign(2*size - 1, NO_OPERATION);
}
void build(const vector<T> &initial){
int _size = int(initial.size());
init(_size);
assert(_size <= size);
build(0, 0, size, initial, _size);
}
void build(int x, int lx, int rx, const vector<T> &initial, int _size){
if(rx - lx == 1){
if(x >= size - 1 && x - size + 1 < _size){
segment_tree[x] = initial[x - size + 1];
}else{
segment_tree[x] = ID;
}
}else{
int mid = (lx + rx)/2;
build(2 * x + 1, lx, mid, initial, _size);
build(2 * x + 2, mid, rx, initial, _size);
segment_tree[x] = combiner_function(segment_tree[2 * x + 1], segment_tree[2 * x + 2]);
}
}
void update(int l, int r, int x, int lx, int rx, H value) {
propogate(x, lx, rx) ;
if( lx >= r || l >= rx ){
return;
}
if( lx >= l && rx <= r){
apply_lazy_on_node(segment_tree[x], value);
apply_lazy_on_change(change[x], value);
return ;
}
int mid = (rx + lx)/2 ;
update(l, r, 2 * x + 1, lx, mid, value);
update(l, r, 2 * x + 2, mid, rx, value);
segment_tree[x] = combiner_function(segment_tree[2 * x + 1], segment_tree[2 * x + 2]) ;
return ;
}
void update(int l, int r, H value) {
update(l, r, 0, 0, size, value) ; return ;
}
T query(int l, int r, int x, int lx, int rx) {
propogate(x, lx, rx) ;
if( lx >= r || l >= rx ){
return NEUTRAL_ELEMENT;
}
if( lx >= l && rx <= r){
return segment_tree[x] ;
}
int mid = (rx + lx)/2 ;
return combiner_function(query(l, r, 2 * x + 1, lx, mid), query(l, r, 2 * x + 2, mid, rx)) ;
}
T query(int l, int r) {
return query(l, r, 0, 0, size) ;
}
};
const int LOG = 25;
#undef int
std::vector<int> countScans(std::vector<int> A,std::vector<int> X,std::vector<int> V){
#define int int64_t
setIO() ;
int n = sz(A), q = sz(X);
vt<int> a(n);
f(i,0,n) a[i] = A[i];
vt<pr<int,int>> query(q);
f(i,0,q){
query[i] = {X[i],V[i]};
}
vt<int> comp;
f(i,0,n){
comp.pb((a[i]<<(int)LOG) + i);
}
for(auto& [i,x]:query){
comp.pb((x<<(int)LOG) + i);
}
sort(all(comp));
comp.erase(unique(all(comp)),comp.end());
int m = sz(comp);
lazy_segment_tree<int,int> st;
st.init(m);
auto add = [&](int i){
int j = lower_bound(all(comp),(a[i]<<(int)LOG) + i) - comp.begin();
//assert(comp[j] == (a[i]<<(int)LOG) + i);
st.update(j+1,m+1,-1);
st.update(j,j+1,i);
};
auto rem = [&](int i){
int j = lower_bound(all(comp),(a[i]<<(int)LOG) + i) - comp.begin();
//assert(comp[j] == (a[i]<<(int)LOG) + i);
st.update(j+1,m+1,1);
st.update(j,j+1,-i);
};
f(i,0,n) add(i);
vt<int> ans;
for(auto [i,x]:query){
rem(i);
a[i] = x;
add(i);
ans.pb(st.query(0,m+1));
}
#undef int
vt<int> _ans(q);
f(i,0,q) _ans[i] = ans[i];
return _ans;
}
/*
#include <cstdio>
#include <cstdlib>
#include <vector>
int readInt(){
int i;
if(scanf("%d",&i)!=1){
fprintf(stderr,"Error while reading input\n");
exit(1);
}
return i;
}
int main(){
int N,Q;
N=readInt();
Q=readInt();
std::vector<int> A(N);
for(int i=0;i<N;i++)
A[i]=readInt();
std::vector<int> X(Q),V(Q);
for(int j=0;j<Q;j++){
X[j]=readInt();
V[j]=readInt();
}
std::vector<int> res=countScans(A,X,V);
for(int j=0;j<int(res.size());j++)
printf("%d\n",res[j]);
}
*/
