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:
# from sys import stdin, stdout
# print = lambda x: stdout.write(x)
# input = stdin.readline
from math import sqrt

#Ref: Geeksforgeeks
def primeFactors(n):
    arr = []
    # Print the number of two's that divide n
    while n % 2 == 0:
        arr.append(2)
        n = n // 2

    # n must be odd at this point
    # so a skip of 2 ( i = i + 2) can be used
    for i in range(3,int(sqrt(n))+1,2):

        # while i divides n , print i ad divide n
        while n % i== 0:
            arr.append(i)
            n = n // i

    # Condition if n is a prime
    # number greater than 2
    if n > 2:
        arr.append(n)
    return arr

def solve(a,n,res):
    for i in res:
        b = n//i
        if a!=b:
            return a,b
    return False

for t in range(int(input())):
    n = int(input())
    res = primeFactors(n)
    if len(res) <= 2:
        print('NO')
        continue
    resset = list(set(res))
    ans = []
    if len(resset) >= 2:
        ans.append(resset[0])
        ans.append(resset[1])
        ans.append(n//(ans[-1]*ans[-2]))
        ans = set(ans)
    else:
        ans.append(resset[0])
        ans.append(resset[0]**2)
        ans.append(n//(ans[-1]*ans[-2]))
        ans = set(ans)
    ans = list(ans)
    if len(ans) == 3 and min(ans)>=2:
        print('YES')
        for i in ans:
            print(i, end = ' ')
        print()
    else:
        print('NO')