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:
t=input()
for p in xrange(t):
    n=input()
    if n<20:
        print "NO"
        continue
    i=2
    k=n
    fac=[]
    d=0
    while i*i<=n and d==0:
        while k%i==0 and k!=0:
            # print k
            k=k/i
            fac.append(i)
            if len(fac)==3:
                d=1
                break
        i+=1
    # print k
    if k!=0 and k!=1:
        fac.append(k)
    # print fac
    if len(fac)<3:
        print 'NO'
        continue
    m=1
    if fac[0]!=fac[1]:
        for i in xrange(2, len(fac)):
            m*=fac[i]
        if m>1 and m!=fac[1] and m!=fac[0]:
            print 'YES'
            print fac[0], fac[1], m
        else:
            print "NO"
    else:
        for i in xrange(3, len(fac)):
            m*=fac[i]
        if fac[1]*fac[2]!=m and m!=fac[0] and m!=1:
            print 'YES'
            print fac[0], fac[1]*fac[2], m
        else:
            print "NO"