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#include <bits/stdc++.h>
using namespace std;
string word;
int nodes = 0;
map<string, int> words;
vector<bool> commas(0);
vector<int> fixed_commas;
vector<string> text;
#include <bits/stdc++.h>
using namespace std;
const int maxn = int(1e5) + 10;
const long long inf = (long long) 1e16;
int n, m, s, vis[maxn], sub[maxn];
vector<pair<int, int>> graph[maxn];
vector<int> path[maxn];
#include "bits/stdc++.h"
using namespace std;
const int MAX = 2000;
const int inf = (int) 1e9;
int n, p, temp;
vector<int> taxi, passenger;
vector<vector<pair<int, int>>> graph(MAX + 5);
#include <bits/stdc++.h>
#define infinite 1152921504606846976
#define base 1000000007
#define maxn 5000500
using namespace std;
int primes[maxn];
long long table[maxn];
#include <bits/stdc++.h>
using namespace std;
vector<int> prime;
int result;
int a, b;
void sieve(int limit) {
bool mark[limit+1];
#include <bits/stdc++.h>
using namespace std;
long long n, l, h;
bool table[1000001];
vector<long long> primes;
long long logarithm(long long a, long long b) {
long long answer = 1;