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 <algorithm>
#include <cstring>
#include <vector>

using namespace std;

bool isprime[1300001];
vector<int> primes;

int main(){
    memset(isprime,true,sizeof(isprime));

    for(int i=2;i<=1300000;++i){
        if(isprime[i]){
            primes.push_back(i);
            for(int j=2;i*j<=1300000;j++){
                isprime[i*j] = false;
            }
        }
    }

    int n;
    while(cin >> n && n){
        if(find(primes.begin(), primes.end(), n) != primes.end()){
            cout << 0 << endl;
        }else{
            vector<int>::iterator it = upper_bound(primes.begin(), primes.end(), n);
            cout << *it - *(it-1) << endl;
        }
    }
}