You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.

If there are several answers, you can print any.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).

Output

For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.

Otherwise, print "YES" and any possible such representation.

Example

Input


5
64
32
97
2
12345


Output


YES
2 4 8 
NO
NO
NO
YES
3 5 823 
import math
ts = int(input( ))
while ts > 0:
    ts = ts - 1
    n = int(input( ))
    flag = 0
    a, b, c = 0, 0, 0
    for i in range( 2, int(math.sqrt(n) + 1 ) ):
        if n % i == 0:
            a = i
            n = int( n / a )
            break
    for i in range( 2, int(math.sqrt(n) + 1 ) ):
        if n % i == 0 and i != a:
            b = i
            n = int( n / b )
            break
    if a != 0 and b != 0:
        c = n
    if c != a and c != b and c != 1 and c != 0:
        print("YES")
        print(a,b,c)
    else:
        print('NO')