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:
d = int(input())

ans = [[0]*3]*d
for i in range(d):
    n = int(input())
    k = int(n**(1/3))+1
    f = True
    j = 2
    while j<k and f:
        if n%j == 0:
            l = n//j
            x = j
            while x<int(l**0.5)+1 and f:
                x+=1
                if l%x == 0 and x!=l//x and j!=l//x:
                    ans[i] = [j,x,l//x]
                    f = False
        j+=1
    if f == True:
        ans[i][0] = -1
for i in range(d):
    if ans[i][0]!=-1:
        print('YES')
        print(ans[i][0],ans[i][1],ans[i][2])
    else:
        print('NO')