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:
for t in range(int(input())):
    n = int(input())
    k = 2
    i = k
    a = -1
    b = -1
    c = -1
    while i <= n/k:
        k+=1
        if n%i == 0:
            a = i
            x = n/a
            break
        else:
            i = k
    if a == -1:
        print("NO")
    else:
        # print(x)
        k = 3
        i = k
        while i <= x/k:
            k+=1
            if x%i == 0 and i != a:
                b = i
                c = x//b
                c = int(c)
                break
            else:
                i = k
        if b == -1 or c == -1:
            print("NO")
        elif a==c or b==c or a==b:
            print("NO")
        else:
            print("YES")
            print(a,b,c)