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:
ans=""
for _ in range(int(input())):
    n=nn=int(input())
    l1=[]; i=2
    while len(l1)<2 and i*i<=nn:
        if n%i==0: l1.append(i); n//=i
        i+=1
    if len(l1)<2 or l1[1]==n or l1[0]==n: ans+="NO\n"
    else: ans+="YES\n"; ans+=f"{l1[0]} {l1[1]} {n}\n"
print(ans)