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:
MOD = 1000000007
MOD2 = 998244353
ii = lambda : int(input())
si = lambda : input()
dgl = lambda : list(map(int, input()))
f = lambda : map(int, input().split())
il = lambda : list(map(int, input().split()))
ls = lambda : list(input())

for _ in range(ii()):
    n=ii()
    fg=0
    oans=[-1,-1,-1]
    for i in range(2,int(n**0.5)+1):
        if n%i==0:
            ans=[-1,-1]
            for j in range(2,int((n//i)**0.5)+1):
                if (n//i)%j==0 and (n//i)//j!=j and j!=i:
                    ans[0]=j
                    ans[1]=(n//i)//j
                    break
            if not -1 in ans and ans[0]!=ans[1]!=i:
                oans[0]=ans[0]
                oans[1]=ans[1]
                oans[2]=i
                fg=1
                break
    if fg:
        print('YES')
        print(*oans)
    else:
        print('NO')