The sequence of n - 1 consecutive composite numbers (positive integers that are not prime and not equal to 1) lying between two successive prime numbers p and p + n is called a prime gap of length n. For example, (24, 25, 26, 27, 28) between 23 and 29 is a prime gap of length 6.

Your mission is to write a program to calculate, for a given positive integer k, the length of the prime gap that contains k. For convenience, the length is considered 0 in case no prime gap contains k.



Input

The input is a sequence of lines each of which contains a single positive integer. Each positive integer is greater than 1 and less than or equal to the 100000th prime number, which is 1299709. The end of the input is indicated by a line containing a single zero.

Output

The output should be composed of lines each of which contains a single non-negative integer. It is the length of the prime gap that contains the corresponding positive integer in the input if it is a composite number, or 0 otherwise. No other characters should occur in the output.

Example

Input

10
11
27
2
492170
0


Output

4
0
6
0
114
#include <bits/stdc++.h>

using namespace std;

#define MAX 1299710
#define SQRTMAX 1141

bool prime[1299709];

int main()
{
    prime[0] = prime[1] = false;
    fill(prime+2, prime+MAX, true);
    for(int p=2; p<SQRTMAX; p++)
    {
        if(prime[p])
        {
            for(int i=2*p; i<MAX; i+=p)
            {
                prime[i] = false;
            }
        }
    }

    int n;
    while(cin >> n, n)
    {
        if(prime[n])
        {
            cout << 0 << endl;
        }
        else
        {
            int f = n;
            int t = n;
            while(!prime[f]) f--;
            while(!prime[t]) t++;
            cout << t - f << endl;
        }

    }
}