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:
def prime_decomposition(n):
    i = 2
    table = []
    while i * i <= n:
        while n % i == 0:
            n /= i
            table.append(i)
        i += 1
    if n > 1:
        table.append(n)
    return table

t = int(input())
for _ in range(t):
    n = int(input())
    ansl = []
    pl = prime_decomposition(n)
    k = 1
    for p in pl:
        k *= p
        if k not in ansl and len(ansl) < 2:
            ansl.append(int(k))
            k = 1
    else:
        if k in ansl or k == 1: 
            print("NO")
            continue
        ansl.append(int(k))
    if len(ansl) < 3:
        print("NO")
    else:
        print("YES")
        print(str(ansl[0])+ " " + str(ansl[1]) + " " + str(ansl[2]))