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:
t = int(input())
for _ in range(t):
    n= int(input())

    import math
    temp = int(math.sqrt(n))
    done = 0
    for i in range(2,temp+1):
        if n%i == 0:
            a = i
            for j in range(2,int(math.sqrt(a))+1):
                if a%j == 0 and a/j != a:
                    x = n//i
                    y = j
                    z = a//j
                    if x!=y and z!=y and z!=x:
                        done = 1
                        break

            if done == 1:
                break

            if i != n/i :
                b = n//i
                for j in range(2,int(math.sqrt(b))+1):
                    if b%j == 0 and b!=b//j:
                        x = i ; y = b//j;z = j
                        if x!=y and z!=y and z!=x:
                            done = 1
                            break
            if done == 1:
                break

    if done:
        print("YES")
        print(x,y,z)
    else:
        print('NO')