Максимум по минимуму

#include <bits/stdc++.h>

using namespace std;

const int N = 1e5 + 3;

int n, m;
int used[N], dist[N], par[N];
vector <int> g[N];

int main(){
    cin >> n >> m;

    int start;
    cin >> start;

    for (int i = 1; i <= m; i++) {
        int a, b;
        cin >> a >> b;
        g[b].push_back(a);
    }

    for (int i = 1; i <= n; i++) {
        dist[i] = -1;
    }

    queue <int> q;
    dist[start] = 0;
    used[start] = 1;
    q.push(start);

    while (!q.empty()) {
        int v = q.front();
        q.pop();
        for (int i = 0; i < g[v].size(); i++) {
            int to = g[v][i];
            if (!used[to]) {
                used[to] = 1;
                dist[to] = dist[v] + 1;
                q.push(to);
            }
        }
    }

    int mx = 0;
    for (int i = 1; i <= n; i++) {
        mx = max(mx, dist[i]);
    }

    cout << mx << endl;
}