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 PYTHON):

Solution:
import math
def factors(n):
    ret = []
    while n % 2 == 0:
        ret.append(2)
        n = n // 2

    for i in range(3, int(math.sqrt(n)) + 1, 2):

        while n % i == 0:
            ret.append(i)
            n = n // i

    if n > 2:
        ret.append(n)

    return ret

for _ in range(int(input())):
    n = int(input())
    pf = factors(n)
    s = set()
    if len(pf)<3:
        print("NO")
    elif len(pf)==3 and len(set(pf))==3:
        print("YES")
        l = map(str,pf)
        print(" ".join(l))
    else:
        s.add(pf[0])
        cnt = pf[1]
        i = 2
        while cnt in s:
            cnt*=pf[i]
            i+=1
        s.add(cnt)
        last = 1
        while i < len(pf):
            last*=pf[i]
            i+=1
        if last in s or last<=1:
            print("NO")
        else:
            print("YES")
            print("{} {} {}".format(pf[0],cnt,last))