#include <stdio.h>
bool primes[1299710];
int main() {
    int i,j,k;for (i=0;i<1299710;primes[i++]=1);for (i=2;i*i<1299709;i++) if (primes[i]) for (j=i*i;j<1299709;primes[j]=0,j+=i);
    while (scanf("%d",&i)!=EOF && i) {k=0;for (j=i;j<1299709 && !primes[j];k++,j++);for (j=i;j>1 && !primes[j];k++,j--);printf("%d\n",k);}
    return 0;}
### Prompt

Please provide a CPP coded solution to the problem described below:

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

### Response

```cpp
#include <stdio.h>
bool primes[1299710];
int main() {
    int i,j,k;for (i=0;i<1299710;primes[i++]=1);for (i=2;i*i<1299709;i++) if (primes[i]) for (j=i*i;j<1299709;primes[j]=0,j+=i);
    while (scanf("%d",&i)!=EOF && i) {k=0;for (j=i;j<1299709 && !primes[j];k++,j++);for (j=i;j>1 && !primes[j];k++,j--);printf("%d\n",k);}
    return 0;}
```