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>
#define MAX 1299711

using namespace std;

bool prime[MAX];

void isPrime(void){

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

int main(void){

  isPrime();

  int p;
  while(cin >> p, p){
    int l,r;
    l = r = p;
    while(!prime[l]) l--;
    while(!prime[r]) r++;
    cout << r - l << endl;;
  }
  return 0;
}