<DSU> TEMPLATE

#include <bits/stdc++.h>
using namespace std;

#define ll long long
#define mp make_pair
#define pb push_back
#define pii pair <int, int>
#define piii pair<pii, int>
#define vi vector<ll>
#define vpii vector<pii>

#define read1(a) int a; scanf("%d", &a)
#define read2(a, b) int a, b; scanf("%d %d", &a, &b)
#define read3(a, b, c) int a, b, c; scanf("%d %d %d", &a, &b, &c)

#define FOR(i, a, b) for (int i=a; i<b; i++)
#define F0R(i, a) for (int i=0; i<a; i++)

#define readgi(n) F0R(i, n) { scanf("%d", &arr[i]); }
#define readgs(n) F0R(i, n) { scanf(" %c", &arr[i]); }

#define f first
#define s second

#define usaco(in, out) freopen(in, "r", stdin); freopen(out, "w", stdout);

#define println1(a) printf("%d\n", a);
#define println2(a, b) printf("%d %d\n", a, b);
#define println3(a, b, c) printf("%d %d %d\n", a, b, c);
#define pv(v) for (int i : v) { printf("%d ", i); } printf("\n");

const int MOD = 1000000007;
const int MAX = 100005;

int idx[MAX];
int sze[MAX];

int root(int x) {
    while (x != idx[x]) {
        idx[x] = idx[idx[x]];
        x = idx[x];
    }
    return x;
}

bool connected(int p, int q) {
    return root(p) == root(q);
}

void join(int p, int q) {
    int i = root(p);
    int j = root(q);
    if (sze[i] < sze[j]) {
        idx[i] = j;
        sze[j] += sze[i];
    }

    else {
        idx[j] = i;
        sze[i] += sze[j];
    }
}

int main() {
    F0R(i, MAX) { idx[i] = i; sze[i] = 1; }
}