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>
#define REP(i,n) for(int i=0;i<(n);i++)
using namespace std;

const int MAX_N = 1300000;
bool prime[MAX_N+1];

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

int main()
{
  sieve();
  while(1){
    int N;
    cin >> N;
    if(N == 0) break;
    if(prime[N]){
      cout << "0" << endl;
      continue;
    }
    int x = N - 1;
    int y = N + 1;
    while(!prime[x])
      x--;
    while(!prime[y])
      y++;
    cout << y - x << endl;
  }
}