#include <iostream>
#include <vector>
#define int long long
using namespace std;
long long collisions(vector<int> x);
int calc(vector<int> arr, int n, int ans = 0) {
vector<int> a(n);
for (auto x : arr)
ans += a[x % n], ++a[x % n];
return ans;
}
int hack() {
vector<int> a;
for (int i = 1; i <= 1e6; ++i) a.push_back(i);
int s = 1, e = 1e6, res = collisions(a);
while (s <= e) {
int n = (s + e) / 2;
int x = calc(a, n);
if (x == res) return n;
if (x < res) e = n - 1;
else s = n + 1;
}
return -1;
}
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