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>
using namespace std;
#define MAX 2000000
bool isP[MAX];
int ans[MAX];

void make_table(){
  for(int i=0;i<MAX;i++)isP[i]=true;
  isP[0]=isP[1]=false;
  for(int i=2;i*i<MAX;i++){
    if(!isP[i])continue;
    for(int j=i*i;j<MAX;j+=i)isP[j]=false;
  }

  for(int i=1;i<MAX;i++){
    if(isP[i])continue;
    ans[i]=ans[i-1]+1;
  }
  for(int i=MAX-2;i>=0;i--){
    if(isP[i])continue;
    ans[i]=max(ans[i],ans[i+1]);
  }
}

int n;
int main(){
  make_table();
  while(1){
    cin>>n;
    if(n==0)break;
    cout<<(ans[n]>0?ans[n]+1:0)<<endl;
  }
  return 0;
}