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#include <bits/stdc++.h>
#include "neutrino.h"

using namespace std;

vector<int> v = {2, 3, 5, 7, 11, 13, 17, 19, 23};

bool isprime(long long x)
{
    long long sqrtx = trunc(sqrt(x));
    for (int i = 2; i <= sqrtx; i++)
        if (x % i == 0)
            return false;
    return true;
}

int main()
{
    vector<bool> prime(100005, true);
    prime[0] = prime[1] = false;
    for (int i = 2; i < 100005; i++)
        if (prime[i] && i * 1ll * i < 100005)
            for (int j = i * i; j < 100005; j += i)
                prime[j] = false;
    vector<int> primes, divs;
    queue<int> q;
    for (int i = 2; i < prime.size(); i++)
        if (prime[i])
            primes.push_back(i);
    long long x = 1, y = 0, res, ans = 1;
    int n = Init();
    for (int i = 0; i < primes.size() && primes[i] <= n; i++)
    {
        if (x * primes[i] > 1e9)
        {
            res = NeutrinoFlow(x, 0);
            x = 1;
            while (!q.empty())
            {
                if (res % q.front() == 0)
                    divs.push_back(q.front());
                q.pop();
            }
        }
        x *= primes[i];
        q.push(primes[i]);
    }
    if (x > 1)
    {
        res = NeutrinoFlow(x, 0);
        while (!q.empty())
        {
            if (res % q.front() == 0)
                divs.push_back(q.front());
            q.pop();
        }
    }
    for (int i = 0; i < divs.size(); i++)
    {
        x = 1;
        while (x * divs[i] <= 1e9)
            x *= divs[i];
        ans *= NeutrinoFlow(x, 0);
    }
    Locate(ans);
    return 0;
}