human
Baby Ehab was toying around with arrays. He has an array a of length n. He defines an array to be good if there's no way to partition it into 2 subsequences such that the sum of the elements in the first is equal to the sum of the elements in the second. Now he wants to remove the minimum number of elements in a so that it becomes a good array. Can you help him?

A sequence b is a subsequence of an array a if b can be obtained from a by deleting some (possibly zero or all) elements. A partitioning of an array is a way to divide it into 2 subsequences such that every element belongs to exactly one subsequence, so you must use all the elements, and you can't share any elements.

Input

The first line contains an integer n (2 ≤ n ≤ 100) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_{n} (1 ≤ a_i ≤ 2000) — the elements of the array a.

Output

The first line should contain the minimum number of elements you need to remove.

The second line should contain the indices of the elements you're removing, separated by spaces.

We can show that an answer always exists. If there are multiple solutions, you can print any.

Examples

Input

4
6 3 9 12

Output

1
2

Input

2
1 2

Output

0

Note

In the first example, you can partition the array into [6,9] and [3,12], so you must remove at least 1 element. Removing 3 is sufficient.

In the second example, the array is already good, so you don't need to remove any elements.
#!/us ... Can you provide a Python code to print any?
assistant
#Here is Python code to print any.
r/bin/env python
import os
import sys
from io import BytesIO, IOBase
import threading 
from bisect import bisect_right
from math import gcd,log
from collections import Counter,defaultdict,deque
from pprint import pprint
from itertools import permutations 
from bisect import bisect_right
from random import randint as rti 
# import deque

def is_pos(arr):
    n=len(arr)
    total=sum(arr)
    if total%2:
        return False
    MX=total//2+1
    pos=[0]*MX
    pos[0]=1
    for i in range(n): 
        for j in range(MX-1-arr[i],-1,-1):
            pos[j+arr[i]]|=pos[j]
        if pos[MX-1]:
            return True
    return False


MOD=10**9+7
def main():
    n=int(input())
    arr=list(map(int,input().split()))
    total=sum(arr)

    if total%2 or (not is_pos(arr)):
        print(0)
        return 
    for i in range(n):
        brr=arr[:i]+arr[i+1:]
        if not is_pos(brr):
            print(1)
            print(i+1)
            return 



        



    

    





        
BUFSIZE = 8192
 
 
class FastIO(IOBase):
    newlines = 0
 
    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
 
    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
 
    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()
 
    def flush(self):
        if...