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;
int prime[10000];
int main(){
	int count=0;
	int i=2;
	while(true){
		bool t=true;
		for(int j=0;j<count;j++){
			if(i%prime[j]==0)
				t=false;
		}
		if(t==true){
			prime[count]=i;
			count++;
		}
		i++;
		if(i==10000)
			break;
	}
	int n;
	while(true){
	cin>>n;
	if(n==0)break;
	int bef,aft;
	bef=n;
	while(true){
		bool t=true;
		for(int i=0;i<count;i++){
			if(bef%prime[i]==0&&bef!=prime[i])
				t=false;
		}
		if(t==true)
			break;
		bef--;
	}
	aft=n;
	while(true){
		bool t=true;
		for(int i=0;i<count;i++){
			if(aft%prime[i]==0&&aft!=prime[i])
				t=false;
		}
		if(t==true)
			break;
		aft++;
	}
	cout<<aft-bef<<endl;
	}
	return 0;
}