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
def make_prime_table(n):
    """n以下の非負整数が素数であるかを判定したリストを出力する
    計算量: O(NloglogN)
    入出力例: 6 -> [False, False, True, True, False, True, False]
    """
    is_prime = [True] * (n + 1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, int(n ** 0.5) + 1):
        if not is_prime[i]:
            continue
        for j in range(2 * i, n + 1, i):
            is_prime[j] = False
    return is_prime


is_prime = make_prime_table(2 * 10 ** 6)
while True:
    n = int(input())
    if n == 0:
        break
    l = n
    r = n
    while not is_prime[l]:
        l -= 1
    while not is_prime[r]:
        r += 1
    print(r - l)
