#include "sorting.h"
#include <bits/stdc++.h>
using namespace std;
//let K_i = n-number of cycles at step i
//f(i) = max(i,K_i) is non decreasing
const int MAXN = 2e5+1;
bool vis[MAXN];
int p[MAXN],q[MAXN];
void change(int i,int j){
int a = p[i];
int b = p[j];
q[a] = j;
q[b] = i;
swap(p[i],p[j]);
}
int findSwapPairs(int n, int S[], int M, int X[], int Y[], int P[], int Q[]) {
vector<int>s(n);
int idx = 0;
bool ok = 1;
for(int i=0;i<n;i++)if(S[i] != i)ok = 0;
if(ok)return 0;
for(int i=0;i<n;i++)s[i] = S[i];
int l = 0,r = M-1;
while(r>=l){
int mid = (l+r)/2;
for(int i=0;i<n;i++)S[i] = s[i];
for(int i=0;i<=mid;i++)swap(S[X[i]],S[Y[i]]);
int cost = n;
for(int j=0;j<n;j++)vis[j] = 0;
for(int j=0;j<n;j++){
int cur = j;
if(vis[j])continue;
while(!vis[cur]){
vis[cur] = 1;
cur = S[cur];
}
cost--;
}
if(cost > mid+1)l = mid+1;
else r = mid-1;
}
idx = l;
for(int i=0;i<n;i++)S[i] = s[i];
for(int i=0;i<=idx;i++)swap(S[X[i]],S[Y[i]]);
vector<array<int,2>>need;
for(int j=0;j<n;j++)vis[j] = 0;
for(int j=0;j<n;j++){
int cur = j;
if(vis[j])continue;
while(!vis[cur]){
vis[cur] = 1;
cur = S[cur];
need.push_back({cur,S[cur]});
}
need.pop_back();
}
//for(auto x:need)cout<<x[0]<<" "<<x[1]<<'\n';
for(int i=0;i<n;i++){
p[i] = s[i];
q[s[i]] = i;
}
reverse(need.begin(),need.end());
for(int i=0;i<=idx;i++){
change(X[i],Y[i]);
if(need.empty()){
P[i] = Q[i] = 0;
continue;
}
//for(int i=0;i<n;i++)cout<<p[i]<<" ";
//cout<<'\n';
int v = need.back()[0];
int u = need.back()[1];
P[i] = q[v];
Q[i] = q[u];
change(q[v],q[u]);
need.pop_back();
//for(int i=0;i<n;i++)cout<<p[i]<<" ";
//cout<<'\n';
}
//for(int i=0;i<n;i++)cout<<p[i]<<" ";
// cout<<'\n';
return idx+1;
}
