**18 人解决**，18 人已尝试。

**20 份提交通过**，共有 24 份提交。

**2.8** EMB 奖励。

**单点时限: **8.0 sec

**内存限制: **256 MB

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 $k$.

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 $100000$-th prime number, which is $1299709$. The end of the input is indicated by a line containing a single zero.

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.

Input

10 11 27 2 492170 0

Output

4 0 6 0 114

**18 人解决**，18 人已尝试。

**20 份提交通过**，共有 24 份提交。

**2.8** EMB 奖励。

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