A. Tile Painting

Ujan has been lazy lately, but now has decided to bring his yard to good shape. First, he decided to paint the path from his house to the gate.

The path consists of nn consecutive tiles, numbered from 11 to nn. Ujan will paint each tile in some color. He will consider the path aesthetic if for any two different tiles with numbers ii and jj, such that |j−i||j−i| is a divisor of nn greater than 11, they have the same color. Formally, the colors of two tiles with numbers ii and jj should be the same if |i−j|>1|i−j|>1 and nmod|i−j|=0nmod|i−j|=0 (where xmodyxmody is the remainder when dividing xx by yy).

Ujan wants to brighten up space. What is the maximum number of different colors that Ujan can use, so that the path is aesthetic?

Input

The first line of input contains a single integer nn (1≤n≤10121≤n≤1012), the length of the path.

Output

Output a single integer, the maximum possible number of colors that the path can be painted in.

Examples

input

Copy

4

output

Copy

2

input

Copy

5

output

Copy

5

Note

In the first sample, two colors is the maximum number. Tiles 11 and 33 should have the same color since 4mod|3−1|=04mod|3−1|=0. Also, tiles 22 and 44 should have the same color since 4mod|4−2|=04mod|4−2|=0.

In the second sample, all five colors can be used.

 递归分解质因数的部分对复杂度有点懵

#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <set>
#include <queue>
#include <map>
#include <sstream>
#include <cstdio>
#include <cstring>
#include <numeric>
#include <cmath>
#include <iomanip>
#include <deque>
#include <bitset>
#include <unordered_set>
#include <unordered_map>
#define ll              long long
#define PII             pair<int, int>
#define rep(i,a,b)      for(int  i=a;i<=b;i++)
#define dec(i,a,b)      for(int  i=a;i>=b;i--)
using namespace std;
int dir[4][2] = { { 0,1 } ,{ 0,-1 },{ 1,0 },{ -1,0 } };
const long long INF = 0x7f7f7f7f7f7f7f7f;
const int inf = 0x3f3f3f3f;
const double pi = 3.14159265358979323846;
const double eps = 1e-6;
const int mod = 998244353;
const int N = 1e6 + 5;
//if(x<0 || x>=r || y<0 || y>=c)

inline ll read()
{
    ll x = 0; bool f = true; char c = getchar();
    while (c < '0' || c > '9') { if (c == '-') f = false; c = getchar(); }
    while (c >= '0' && c <= '9') x = (x << 1) + (x << 3) + (c ^ 48), c = getchar();
    return f ? x : -x;
}
ll gcd(ll m, ll n)
{
    return n == 0 ? m : gcd(n, m % n);
}
ll lcm(ll m, ll n)
{
    return m * n / gcd(m, n);
}
bool isprime(ll x)
{
    for (int i = 2; i <= sqrt(x); i++)
    {
        if (x % i == 0)
            return 0;
    }
    return 1;
}
vector<int> vis(N + 5),pri;
void sieve()
{
    for (int i = 2; i < N; i++)
    {
        if (!vis[i])
            pri.push_back(i);
        for (int x : pri)
        {
            if ((ll)i * x > N)
                break;
            vis[i * x] = 1;
            if (i % x == 0)
                break;
        }
    }
}
ll n,ans,cnt;
void work(ll now)
{
    for (int d : pri)
    {
        if ((ll)d * d > now)
            break;
        if (now % d == 0)
        {
            ans = min(ans, (ll)d);
            cnt++;
            while (now % d == 0)
                now /= d;
            work(now);
            break;
        }
    }
    if (now != 1)
        ans = min(ans, now), cnt++;
}
int main()
{
    sieve();
    cin >> n;
    ans = n;
    work(n);
    if (cnt >= 2)
        cout << 1 << endl;
    else
        cout << ans << endl;
    return 0;
}