Today Hayato came home from school with homework.

In the assignment, Hayato was given an array $a$ of length $n$. The task was to find $3$ numbers in this array whose sum is odd. At school, he claimed that there are such $3$ numbers, but Hayato was not sure, so he asked you for help.

Answer if there are such three numbers, and if so, output indices $i$, $j$, and $k$ such that $a_i + a_j + a_k$ is odd.

The odd numbers are integers that are not divisible by $2$: $1$, $3$, $5$, and so on.


-----Input-----

The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

For each test case, the first line contains one integer $n$ ($3 \le n \le 300$) — the length of $a$.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^5$) — the array $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot10^5$.


-----Output-----

For each test case, in the first line print one word "YES" (without quotes) if there are $3$ numbers with an odd sum or "NO" (without quotes) if there are no such $3$ numbers.

If the answer exists, then on the second line print $3$ distinct integers $i, j, k$ ($1 \le i, j, k \le n$) — the indices of the numbers. If there are several answers, output any.


-----Examples-----

Input
6
3
1 1 1
4
1 1 2 2
3
1 2 3
5
1 4 5 1 2
4
2 6 2 4
5
5 6 3 2 1
Output
YES
1 2 3
YES
3 4 1
NO
YES
1 3 4
NO
YES
1 3 5


-----Note-----

In the first test case, there is one way to choose $3$ numbers, and since $1 + 1 + 1 = 3$, this triple is fine for us.

In the second test case, you need to choose the numbers $1, 2, 2$, since $1 + 2 + 2 = 5$.

In the third test case, there is one way to choose three numbers, but $1 + 2 + 3 = 6$ is an even number, so the required triple does not exist.

In the fifth test case, no matter what three numbers we choose, their sum is even.

Difficulty: EASY

Solutions:
def program():
	n = int(input())
	a = [int(x) for x in input().split()]
	indices_odd = []
	indices_even = []
	answer = ''
	for i in range(0, len(a)):
		if a[i] % 2 != 0:
			indices_odd.append(str(i + 1))
			if len(indices_odd) == 3:
				break
		elif len(indices_even) < 2:
			indices_even.append(str(i + 1))
	if len(indices_odd) == 3:
		for i in range(0, len(indices_odd)):
			if i == len(indices_odd) - 1:
				answer = answer + indices_odd[i]
			else:
				answer = answer + indices_odd[i] + ' '
		answers.append(('YES', answer))
	elif len(indices_odd) >= 1 and len(indices_even) >= 2:
		for i in range(0, len(indices_even)):
			answer = answer + indices_even[i] + ' '
		answer = answer + indices_odd[0]
		answers.append(('YES', answer))
	else:
		answers.append(('NO', ''))
t = int(input())
answers = []
for i in range(0, t):
	program()
for i in answers:
	if i[0] == 'YES':
		print(i[0])
		print(i[1])
	else:
		print(i[0])


import sys
input = sys.stdin.readline
T = int(input())
for i in range(T):
	N = int(input())
	arr = list(map(int, input().split()))
	h = []
	z = []
	for a in range(N):
		if arr[a] % 2 == 0:
			z.append(a + 1)
		else:
			h.append(a + 1)
	if len(h) > 2:
		print('YES')
		print(' '.join(map(str, h[:3])))
	elif len(h) > 0 and len(z) > 1:
		print('YES')
		print(z[0], z[1], h[0])
	else:
		print('NO')


for i in range(int(input())):
	n = int(input())
	a = list(map(int, input().split()))
	(e, o) = ([], [])
	for i in range(n):
		if a[i] % 2 == 0:
			e.append(i + 1)
		else:
			o.append(i + 1)
	if o == []:
		print('NO')
	elif len(e) == 1 and n == 3:
		print('NO')
	else:
		print('YES')
		if len(o) >= 3:
			print(*o[:3])
		else:
			print(e[0], e[1], o[0])


import os.path
from math import gcd, floor, ceil
from collections import *
import sys
mod = 1000000007
INF = float('inf')

def st():
	return list(sys.stdin.readline().strip())

def li():
	return list(map(int, sys.stdin.readline().split()))

def mp():
	return map(int, sys.stdin.readline().split())

def inp():
	return int(sys.stdin.readline())

def pr(n):
	return sys.stdout.write(str(n) + '\n')

def prl(n):
	return sys.stdout.write(str(n) + ' ')
if os.path.exists('input.txt'):
	sys.stdin = open('input.txt', 'r')
	sys.stdout = open('output.txt', 'w')
t = inp()
for i in range(t):
	n = inp()
	l = li()
	(k, k1) = (0, 0)
	(l1, l2) = ([], [])
	for i in range(n):
		if l[i] % 2 == 0 and k < 2:
			l1.append(i + 1)
			k += 1
		elif l[i] % 2 != 0 and k1 < 3:
			l2.append(i + 1)
			k1 += 1
	if len(l2) == 3:
		print('YES')
		print(*l2)
	elif len(l1) == 2 and len(l2) >= 1:
		print('YES')
		print(l1[0], l1[1], l2[0])
	else:
		print('NO')


tests = int(input())
main_list = []
for i in range(tests):
	input()
	a = list(map(int, input().split()))
	main_list.append(a)
ans_list = []
yes_no = []
for i in main_list:
	even = []
	odd = []
	for num in range(len(i)):
		if i[num] % 2 == 0:
			even.append(num + 1)
		else:
			odd.append(num + 1)
	if len(odd) >= 3:
		print('YES')
		print(f'{odd[0]} {odd[1]} {odd[2]}')
	elif len(odd) >= 1 and len(even) >= 2:
		print('YES')
		print(f'{even[0]} {even[1]} {odd[0]}')
	else:
		print('NO')


def exe():
	le = []
	lo = []
	for i in range(n):
		if lst[i] % 2 == 0:
			le += [i + 1]
		else:
			lo += [i + 1]
	if len(lo) >= 3:
		print('YES')
		print(lo[0], lo[1], end=' ')
		return lo[2]
	elif len(le) >= 2 and len(lo) >= 1:
		print('YES')
		print(le[0], le[1], end=' ')
		return lo[0]
	else:
		return 'NO'
for i in range(int(input())):
	n = int(input())
	lst = list(map(int, input().split()))
	print(exe())


t = int(input())
for _ in range(t):
	n = int(input())
	a = list(map(int, input().split()))
	l = []
	s = []
	for i in range(n):
		if a[i] % 2 == 0:
			l.append(i)
		else:
			s.append(i)
	if len(s) > 2:
		print('YES')
		print(s[0] + 1, s[1] + 1, s[2] + 1)
	elif len(s) == 1 and len(l) > 1 or (len(s) > 0 and len(l) > 1):
		print('YES')
		print(l[0] + 1, l[1] + 1, s[0] + 1)
	else:
		print('NO')


def solve():
	n = int(input())
	a = list(map(int, input().split()))
	(eve, od) = ([], [])
	for i in range(n):
		if a[i] % 2 == 0:
			eve.append(i + 1)
		else:
			od.append(i + 1)
	if od == []:
		print('NO')
	elif len(eve) == 1 and n == 3:
		print('NO')
	else:
		print('YES')
		if len(od) >= 3:
			print(*od[:3])
		else:
			print(eve[0], eve[1], od[0])
for i in range(int(input())):
	solve()