Hash Function

题号：NC223597
时间限制：C/C++/Rust/Pascal 2秒，其他语言4秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
64bit IO Format: %lld

题目描述

For a given set $S = \{a_0, a_1, a_2, ..., a_{n-1}\}$ , we called a hash function $f_S(x)$ perfect hash function of S, if it satisfies $\forall 0 \leq i < j < n, f_S(a_i) \neq f_S(a_j)$ .

Given a set S with non-negative integers, please find the minimum positive integer seed that function $h_{seed}(x) = x \mod seed$ is a perfect hash function of S.

Note: Six more test cases are added after contest.

输入描述:

The first line of input contains one integer $n$, describing the size of set S.

The second line contains  integers , describing the elements in S.

It is guaranteed that .

输出描述:

Output one integer in a line, indicating the answer.

示例1

输入

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3
2 3 4

输出

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示例2

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3
1 2 4

输出

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示例3

输入

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10
0 7 23 18 29 27 6 28 24 11

输出

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