#include <bits/stdc++.h>
using namespace std;
#define FOR(i,s,e) for(int i = s; i <= (int)e; ++i)
#define DEC(i,s,e) for(int i = s; i >= (int)e; --i)
#define IAMSPEED ios_base::sync_with_stdio(false); cin.tie(0);
#ifdef LOCAL
#define db(x) cerr << #x << "=" << x << "\n"
#define db2(x, y) cerr << #x << "=" << x << " , " << #y << "=" << y << "\n"
#define db3(a,b,c) cerr<<#a<<"="<<a<<","<<#b<<"="<<b<<","<<#c<<"="<<c<<"\n"
#define dbv(v) cerr << #v << ":"; for (auto ite : v) cerr << ite << ' '; cerr <<"\n"
#define dbvp(v) cerr << #v << ":"; for (auto ite : v) cerr << "{" << ite.f << ',' << ite.s << "} "; cerr << "\n"
#define dba(a,ss,ee) cerr << #a << ":"; FOR(ite,ss,ee) cerr << a[ite] << ' '; cerr << "\n"
#define reach cerr << "LINE: " << __LINE__ << "\n";
#else
#define reach
#define db(x)
#define db2(x,y)
#define db3(a,b,c)
#define dbv(v)
#define dbvp(v)
#define dba(a,ss,ee)
#endif
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#define pb push_back
#define eb emplace_back
#define all(x) (x).begin(), (x).end()
#define f first
#define s second
#define g0(x) get<0>(x)
#define g1(x) get<1>(x)
#define g2(x) get<2>(x)
#define g3(x) get<3>(x)
typedef pair <int, int> pi;
typedef tuple<int,int,int> ti3;
typedef tuple<int,int,int,int> ti4;
int rand(int a, int b) { return a + rng() % (b-a+1); }
const int MOD = 1e9 + 7;
const int inf = (int)1e9 + 500;
const long long oo = (long long)1e18 + 500;
template <typename T> void chmax(T& a, const T b) { a=max(a,b); }
template <typename T> void chmin(T& a, const T b) { a=min(a,b); }
const int MAXN = 200005;
int A[MAXN];
int n,m;
int X[MAXN], Y[MAXN];
int idx[MAXN];
struct ufds_{
int p[MAXN],sz[MAXN];
ufds_() {
iota(p,p+MAXN,0);
fill(sz,sz+MAXN,1);
}
int find(int x) {
if(x==p[x])return x;
else return p[x]=find(p[x]);
}
void merge(int x, int y) {
x=find(x);y=find(y);
if(x==y)return;
if(sz[x]>=sz[y]){
sz[x]+=sz[y];
p[y]=x;
} else {
sz[y]+=sz[x];
p[x]=y;
}
}
};
bool check(int ti) {
//you can use ti operations to do everything
FOR(i,0,ti-1) {
swap(A[X[i]],A[Y[i]]);
}
FOR(i,0,n-1){
idx[A[i]]=i;
}
db(ti);
int res = 0;
dba(A,0,n-1);
FOR(i,0,n-1) {
int y=idx[i];
db2(i,y);
if(i==y)continue;
else {
// swap index i to index y.
db2(i,y);
++res;
swap(A[i],A[y]);
swap(idx[A[i]],idx[A[y]]);
}
}
return res<=ti;
}
int findSwapPairs(int n, int S[], int M, int X[], int Y[], int P[], int Q[]) {
//FOR(i,0,n-1)A[i]=S[i];
::n=n;
::m=M;
FOR(i,0,m-1)::X[i]=X[i];
FOR(i,0,m-1)::Y[i]=Y[i];
int lo=-1, hi=m+1;
while(lo<hi-1) {
FOR(i,0,n-1)A[i]=S[i];
int mid=(lo+hi)/2;
db(mid);
if(check(mid))hi=mid;
else lo=mid;
}
int R=hi;
db(R);
// i am doing R number of operations.
FOR(i,0,n-1)A[i]=S[i];
FOR(i,0,R-1) {
swap(A[X[i]],A[Y[i]]);
}
vector<pi> ops;
FOR(i,0,n-1){
idx[A[i]]=i;
}
FOR(i,0,n-1) {
int y=idx[i];
if(i==y)continue;
else {
// swap index i to index y.
ops.pb({A[i],A[y]});
swap(A[i],A[y]);
swap(idx[A[i]],idx[A[y]]);
}
}
reverse(all(ops));
FOR(i,0,n-1)A[i]=S[i];
FOR(i,0,n-1)idx[A[i]]=i;
FOR(i,0,R-1) {
pi cur=ops.back(); ops.pop_back();
int val1=cur.f, val2=cur.s;
int Aidx=idx[val1], Bidx=idx[val2];
P[i]=Aidx; Q[i]=Bidx;
swap(A[Aidx],A[Bidx]);
swap(idx[val1],idx[val2]);
swap(A[X[i]],A[Y[i]]);
swap(idx[A[X[i]]], idx[A[Y[i]]]);
dba(A,0,n-1);
}
return R;
}
