human
Despite his bad reputation, Captain Flint is a friendly person (at least, friendly to animals). Now Captain Flint is searching worthy sailors to join his new crew (solely for peaceful purposes). A sailor is considered as worthy if he can solve Flint's task.

Recently, out of blue Captain Flint has been interested in math and even defined a new class of integers. Let's define a positive integer x as nearly prime if it can be represented as p ⋅ q, where 1 < p < q and p and q are prime numbers. For example, integers 6 and 10 are nearly primes (since 2 ⋅ 3 = 6 and 2 ⋅ 5 = 10), but integers 1, 3, 4, 16, 17 or 44 are not.

Captain Flint guessed an integer n and asked you: can you represent it as the sum of 4 different positive integers where at least 3 of them should be nearly prime.

Uncle Bogdan easily solved the task and joined the crew. Can you do the same?

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.

Next t lines contain test cases — one per line. The first and only line of each test case contains the single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number Flint guessed.

Output

For each test case print: 

  * YES and 4 different positive integers such that at least 3 of them are nearly prime and their sum is equal to n (if there are multiple answers print any of them).

  * NO if there is no way to represent n as the sum of 4 different positive integers where at least 3 of them are nearly prime. 

You can print each character of YES or NO in any case.

Example

Input

7
7
23
31
36
44
100
258

Output

NO
NO
YES
14 10 6 1
YES
5 6 10 15
YES
6 7 10 21
YES
2 10 33 55
YES
10 21 221 6

Note

In the first and second test cases, it can be proven that there are no four different positive integers such that at least three of them are nearly prime.

In the third test case, n=31=2 ⋅ 7 + 2 ⋅ 5 + 2 ⋅ 3 + 1: integers 14, 10, 6 are nearly prime.

In the fourth test case, n=36=5 + 2 ⋅ 3 + 2 ⋅ 5 + 3 ⋅ 5: integers 6, 10, 15 are nearly prime.

In the fifth test case, n=44=2 ⋅ 3 + 7 +...
assistant
#Here is Python code to print any of them).

#from __future__ import print_function
mod=int(1e9+7)
#import resource
#resource.setrlimit(resource.RLIMIT_STACK, [0x100000000, resource.RLIM_INFINITY])
#import threading
#threading.stack_size(2**25)
#import sys
#sys.setrecursionlimit(10**5)
#fact=[1]
#for i in range(1,100001):
#    fact.append((fact[-1]*i)%mod)
#ifact=[0]*100001
#ifact[100000]=pow(fact[100000],mod-2,mod)
#for i in range(100000,0,-1):
#    ifact[i-1]=(i*ifact[i])%mod
#from random import randint as rn
import bisect
from bisect import bisect_left as bl              #c++ lowerbound bl(array,element)
from bisect import bisect_right as br             #c++ upperbound
import itertools
import collections
import math
import heapq
from types import GeneratorType
def bootstrap(f, stack=[]):
    def wrappedfunc(*args, **kwargs):
        if stack:
            return f(*args, **kwargs)
        else:
            to = f(*args, **kwargs)
            while True:
                if type(to) is GeneratorType:
                    stack.append(to)
                    to = next(to)
                else:
                    stack.pop()
                    if not stack:
                        break
                    to = stack[-1].send(to)
            return to
    return wrappedfunc
def modinv(n,p):
    return pow(n,p-2,p)
def ncr(n,r,p):                        #for using this uncomment the lines calculating fact and ifact
    t=((fact[n])*((ifact[r]*ifact[n-r])%p))%p
    return t
def GCD(x,y):
    while(y):
        x, y = y, x % y
    return x
def ain():                           #takes array as input
    return list(map(int,sin().split()))
def sin():
    return input()
range=xrange
intmax=10**18
"""*******************************************************"""
def main():
    for _ in range(int(sin())):
        n=int(sin())
        if(n<=30):
            print"NO"
            continue
        print "YES"
        if(n==36 or n==40 or n==44):
            print 6,10,15,n-31
        else:
            print 6,10,14,n-30
######## Python 2 and 3 footer by Pajenegod and...