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


def div(n, r):
    sq = math.sqrt(n)
    d = 1
    for x in range(2, int(sq) + 1):
        if n % x == 0 and x != r:
            d = x
            break
    return d


t = int(input())
for i in range(0, t):
    y = int(input())
    a = div(y, 1)
    if a == 1:
        print("NO")
        continue
    else:
        z = int(y / a)
        b = div(z, a)
        if b == 1 or b == a:
            print("NO")
            continue
        else:
            c = int(y / (a * b))
            if c == 1 or c == a or c == b:
                print("NO")
                continue
            else:
                print("YES")
                print(a, b, c)
