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<iostream>
#include<cmath>
using namespace std;

bool judgePrimeNumber( int a )
{
    for( int i = 2; i <= sqrt(a); i++ )
        if( a % i == 0 )
            return false;
    return true;
}

int main()
{
    int n;

    while( cin >> n )
    {
        if( n == 0 )
            break;
        if( judgePrimeNumber(n) )
            cout << 0 << endl;
        else
        {
            int a = n + 1, b = n - 1;
            while( judgePrimeNumber(a) == false )
                a++;
            while( judgePrimeNumber(b) == false )
                b--;
            cout << a - b << endl;
        }
    }
    return 0;
}

