Given a number N. You are tasked with finding the smallest number S, such that N is a factor of S! (S factorial). N can be very large.

**Input:**

The first line of input contains an integer T denoting the number of test cases. Then T test cases follow. Each test case contains an integer n.

**Output:**

Print the smallest number, such that N is a factor of S!

**Constraints:**

1<=T<=100

1<=N<=10^12

**Example:**

Input:

2

6

800

**Output:**

3

10

#### **For More Examples Use Expected Output**