Given a positive integer n. Find three distinct positive integers a, b, c such that a + b + c = n and \operatorname{gcd}(a, b) = c, where \operatorname{gcd}(x, y) denotes the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of integers x and y.

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. Description of the test cases follows.

The first and only line of each test case contains a single integer n (10 ≤ n ≤ 10^9).

Output

For each test case, output three distinct positive integers a, b, c satisfying the requirements. If there are multiple solutions, you can print any. We can show that an answer always exists.

Example

Input


6
18
63
73
91
438
122690412


Output


6 9 3
21 39 3
29 43 1
49 35 7
146 219 73
28622 122661788 2

Note

In the first test case, 6 + 9 + 3 = 18 and \operatorname{gcd}(6, 9) = 3.

In the second test case, 21 + 39 + 3 = 63 and \operatorname{gcd}(21, 39) = 3.

In the third test case, 29 + 43 + 1 = 73 and \operatorname{gcd}(29, 43) = 1.
1
669278611
 10
10
52
91
23
44
99
28
54
99
51

334639303 334639307 1
 4 5 1
25 26 1
43 47 1
9 13 1
21 22 1
47 51 1
13 14 1
26 27 1
47 51 1
23 27 1

import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, functools,copy,random
from functools import reduce 
import operator
 

inf = 10**9+7
mod = (10**9+7)
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def LS(): return input().split()
def endl(): return print('\n')
def lcm(a,b): return (a*b) // math.gcd(a,b)
def grayCode (n): return n ^ (n >> 1);
sys.setrecursionlimit(20000)    # adjust numbers
graph = collections.defaultdict(list)
grid = []
visited = set()
ways = ["D","U","R","L"]
dx =   [1,-1,0,0]
dy =   [0,0,1,-1]
#0
def find(i) :
    if par[i] != i : par[i] = find(par[i]);
    return par[i]
def union(a, b) :
    a = find(a)
    b = find(b)
    if a == b : return False
    par[a] = b
    return True
#par = [i for i in range(n)]
def initGraph(m):
    for _ in range(m):
        u,v = LI()
        graph[u-1].append(v-1)
        graph[v-1].append(u-1)
    return graph
def initGraphW(m):
    for _ in range(m):
        a,b,c = LI()
        graph[a-1].append((b-1,c))
        graph[b-1].append((a-1,c))
 
def initGrid(h,w):
    for i in range(h):
        s = S()
        grid.append(list(s))
    return grid
 
def soe(limit):
    a = [True] * limit                          # Initialize the primality list
    a[0] = a[1] = False
 
    for (i, isprime) in enumerate(a):
        if isprime:
            yield i
            for n in range(i*i, limit, i):     # Mark factors non-prime
                a[n] = False
    return a

################## Main (Author - 9th) ################## 

for _ in range(I()):
    n = I()
    if n%2 == 0:
        print(n-3, 2, 1)
    else:
        print(n-4, 3, 1)