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;
#define KMAX 2299709

bool isprime[KMAX];

void cp(){
  for(int i=0; i < KMAX; i++){
    isprime[i] = true;
  }
  isprime[0] = isprime[1] = false;
  for(int i = 2; i*i <= KMAX; i++){
    if(isprime[i]){
      for(int j = i+i; j < KMAX; j += i){
        isprime[j] = false;
      }
    }
  }
}

int main(void){
  ios::sync_with_stdio(false);
  cin.tie(0);
  cp();
  int k;
  while(cin >> k, k){
    int a, b;
    for(int i = k; i >= 0; i--){
      if(isprime[i]){
        a = i;
        break;
      }
    }
    for(int i = k; i < KMAX; i++){
      if(isprime[i]){
        b = i;
        break;
      }
    }
    cout << b - a << endl;
  }
  return 0;
}