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

t = int(input())
while t>0:
    t-=1
    n = int(input())
    sn = n
    l = []
    for i in range(2,int(math.sqrt(n))+1):
        if n%i == 0:
            l.append(i)
            n = n//i
            c = i
            break
    else:
        print("NO")
        continue

    for i in range(c+1,int(math.sqrt(n))+1):
        if n%i == 0:
            l.append(i)
            n = n//i
            break
    else:
        print("NO")
        continue

    if (sn//(l[0]*l[1]))!=1 and (sn//(l[0]*l[1]) not in l):
        l.append(sn//(l[0]*l[1]))
        print("YES")
        print(*l)
    else:
        print("NO")