# GCDS - Sabbir and gcd problem

## 题意翻译

- 给定 $n$ 个整数 $a_i$，找到最小的整数 $x$ 使得他与所有的 $a_i$ 都互质且 $x>1$。 - **多组数据**，$1 \le t \le 10$。 - 对于 $100\%$ 的数据，$1 \le n \le 10^5$，$1 \le a_i \le 10^7$。 - Translated by 一只书虫仔。

## 题目描述

Sabbir is a little boy. He loves math very much. one day his friend taskin gave him a very hard task. taskin gave him _**n**_ numbers _**a $_{1}$ ,a $_{2}$ ,a $_{3}$ ,......a $_{n}$**_ taskin asked for a minimum integer number _**x**_ (**x > 1**) such that _**gcd(x,a $_{1}$ ) = 1, gcd(x,a $_{2}$ ) = 1, ...... gcd(x,a $_{n}$ ) = 1**_, in other words you have to find a minimum integer _**_x_ ( x > 1 )**_ such that [**![](https://cdn.luogu.com.cn/upload/vjudge_pic/SP30919/9a61eb88995ea804d556f658307451f21ac90d9b.png)&space;=&space;1 "\forall i ,\ i\epsilon [1....n] ,\ gcd(x,a_{i}) = 1")**](https://www.codecogs.com/eqnedit.php?latex=\forall&space;i&space;,\&space;i\epsilon&space;[1....n]&space;,\&space;gcd(x,a_{i})&space;=&space;1) **Note:** **gcd is greatest common divisor**

## 输入输出格式

### 输入格式

In the first line there will be an integer **T ,** denoting the number of test cases, each test case is consists of 2 lines.. in the first line there will be **n ,** denoting the number of integers and next line contains **n** space separated integers **$a _ 1, a _ 2, \cdots, a _ n$** [![](https://latex.codecogs.com/gif.latex?1&space;\leq&space;T&space;\leq&space;10 "1 \leq T \leq 10")](https://www.codecogs.com/eqnedit.php?latex=1&space;\leq&space;T&space;\leq&space;10) [![](https://latex.codecogs.com/gif.latex?1&space;\leq&space;n&space;\leq&space;10^{5} "1 \leq n \leq 10^{5}")](https://www.codecogs.com/eqnedit.php?latex=1&space;\leq&space;n&space;\leq&space;10^{5}) [](https://www.codecogs.com/eqnedit.php?latex=1&space;\leq&space;n&space;\leq&space;10^{5}) [![](https://latex.codecogs.com/gif.latex?1&space;\leq&space;a_{i}&space;\leq&space;10^{7} "1 \leq a_{i} \leq 10^{7}")](https://www.codecogs.com/eqnedit.php?latex=1&space;\leq&space;a_{i}&space;\leq&space;10^{7})

### 输出格式

for every case print one integer **x** in one line . Note: **x** should be greater than 1.

## 输入输出样例

### 输入样例 #1

3
3
5 7 25
4
1 2 3 4
1
2

### 输出样例 #1

2
5
3