Problem: 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 

Solution (in PYTHON3):

Solution:
import math

def div(n):
    l = []
    i = 2
    while i <= math.sqrt(n):
        if (n % i == 0):
            if (n / i == i):
                l.append(int(i))
            else:
                l.append(int(i))
                l.append(int(n/i))

        i = i + 1

    l.sort()
    return l

for _ in range(int(input())):
    n = int(input())
    y = n
    l = div(n)
    l = l[::-1]
    #print(l)
    o = []
    if len(l) != 0:
        y = y//l[-1]
        x1 = l[-1]
        o.append(l[-1])
        l.pop()

    else:
        print("NO")
        continue

    if len(l) != 0:
        f = 1
        while(f == 1 and (y % l[-1] != 0)):
            l.pop()
            if len(l) == 0:
                f = 0

        if f == 0:
            print("NO")
            continue

        y = y // l[-1]
        o.append(l[-1])
        x2 = l[-1]
        l.pop()

        if len(l) == 0:
            print("NO")
            continue

        if (x2 == y) or (x1 == x2) or (x1 == y) or (x1 == 1) or (x2 == 1) or (y == 1):
            print("NO")
            continue

        o.append(y)

    else:
        print("NO")
        continue

    cnt = 1
    for i in o:
        cnt = cnt*i

    if cnt == n:
        print("YES")
        for i in o:
            print(i,end = " ")

        print("")

    else:
        print("NO")