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This task is the inverse of ETF problem, given an integer n find smallest integer i such that φ(i)=n, where φ denotes Euler's totient function.

Input

The first line is an integer T(1 ≤ T ≤ 100,000), denoting the number of test cases. Then, T test cases follow.

For each test case, there is an integer n(1 ≤ n ≤ 100,000,000) written in one line. (one ineger per line)

Output

For each test case, output Smallest Inverse Euler's Totient Function of n. if n doesn't have inverse, output -1.

Example

Input:

5

10

20

30

40

50
Output:

11

25

31

41

-1

Time Limit ≈ 3*(My Program Top Speed)

See also: Another problem added by Tjandra Satria Gunawan