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<stdio.h>
#include<algorithm>
using namespace std;
int prime[1299709];
int table[100000];

int main(){
	prime[0]=1;
	for(int i=1;i<1299709;i++){
		if(prime[i]==0){
			prime[i]=1;
			for(int j=(i+1)*2-1;j<=1299709;j+=i+1)prime[j]=2;
		}
	}
	int now=0;
	for(int i=0;i<1299709;i++){
		if(prime[i]==1){
			table[now++]=i+1;
		}
	}
	int a;

	while(1){
		scanf("%d",&a);
		if(a==0)return 0;
		int index=(int)(lower_bound(table,table+100000,a)-table);
		if(table[index]==a)printf("0\n");
		else printf("%d\n",table[index]-table[index-1]);
	}
}