#pragma g++ optimize("Ofast")
#include <bits/stdc++.h>
#define pb emplace_back
#define get_pos(u,x) (lower_bound(begin(u),end(u),x) - begin(u))
using namespace std;
const int N = 500025;
struct Segtree {
int mx[N<<1],lz[N],n;
void init(auto &&v, int _n) {
n = _n;
for(int i = 0; i < n; i++) mx[i+n] = v[i], lz[i] = 0;
for(int i = n-1; i > 0; i--) mx[i] = max(mx[i<<1], mx[i<<1|1]);
}
void upd(int p, int d) {
mx[p] += d;
if(p < n) lz[p] += d;
}
void pull(int p) {
for(; p>1; p>>=1) mx[p>>1] = max(mx[p],mx[p^1]) + lz[p>>1];
}
void push(int p) {
for(int h = __lg(n); h >= 0; h--) {
int i = p>>h;
if(!lz[i>>1]) continue;
upd(i,lz[i>>1]);
upd(i^1,lz[i>>1]);
lz[i>>1] = 0;
}
}
void add(int l, int r, int d) {
int L = l, R = r;
for(l+=n,r+=n; l<r; l>>=1,r>>=1) {
if(l&1) upd(l++, d);
if(r&1) upd(--r, d);
}
pull(L+n), pull(R-1+n);
}
int query(int l, int r) {
int res = -1e9;
push(l+n), push(r-1+n);
for(l+=n,r+=n; l<r; l>>=1,r>>=1) {
if(l&1) res = max(res, mx[l++]);
if(r&1) res = max(res, mx[--r]);
}
return res;
}
/*void dbg() {
cout << "-------\n";
for(int i = 0; i < 10; i++) {
push(i+N);
cout << mx[i+N] << ' ';
}
cout << '\n';
}*/
} sgt;
vector<int> countScans(vector<int> A, vector<int> X, vector<int> V) {
int n = A.size(), q = X.size();
vector<pair<long long,int>> u;
for(int i = 0; i < n; i++) u.pb(1LL * A[i] * N + i, i);
for(int i = 0; i < q; i++) u.pb(1LL * V[i] * N + X[i], i+n);
sort(u.begin(), u.end());
long long last = u.front().first;
int j = 0;
for(auto [val, id]: u) {
if(val != last) ++j;
if(id < n)
A[id] = j;
else
V[id-n] = j;
last = val;
}
vector<int> Q(q), S(j);
for(int i = 0; i < n; i++) if(A[i] < j) --S[A[i]+1];
for(int i = 1; i < j; i++) S[i] += S[i-1];
for(int i = 0; i < n; i++) S[A[i]] += i;
sgt.init(S, j);
for(int i = 0; i < q; i++) {
int x = X[i];
sgt.add(A[x],A[x]+1, -x);
sgt.add(A[x]+1, j, 1);
A[x] = V[i];
sgt.add(A[x],A[x]+1, x);
sgt.add(A[x]+1, j, -1);
//sgt.dbg();
Q[i] = sgt.mx[1];
}
return Q;
}
