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>

using namespace std;

static constexpr auto Limit = 2000000;

int main()
{
    bool marked[Limit] = { true, true };
    bool is_prime[Limit] = {};

    for( int i=0; i<Limit; ++i ) {
        if ( marked[i] || is_prime[i] )
            continue;
        
        is_prime[i] = true;
        
        for( int j=i; j<Limit; j+=i ) {
            marked[j] = true;
        }
    }

    int n;
    while( cin >> n ) {
        if ( n == 0 )
            break;

        int gap = 0;
        if ( !is_prime[n] ) {
            while( !is_prime[--n] );

            ++gap;
            while( !is_prime[++n] )
                ++gap;
        }
        cout << gap << endl;
    }
}