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 x in range(t):
    n = int(input())
    i = 2
    rt = int(n**0.5)
    l = []
    dp = [True]*(int(n**0.5)+1)
    while i <= rt and len(l) < 3:
        if n%i!=0:
            i+=1
        else:
            if dp[i]:
                l.append(i)
                dp[i] = False
                if len(l) == 2:
                    if l[0] != n//i and i != n//i:
                        l.append(n//i)
                n = n//i
                rt = int(n**0.5)
                i = 2
            else:
                i += 1
    if len(l) == 3:
        print("YES")
        print(l[0], l[1], l[2])
    else:
        print("NO")