1516_C. Baby Ehab Partitions Again
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.
```python
import collections
import itertools
from functools import reduce

mod = (10 ** 9) + 7


def permutationbysum():
    for _ in range(int(input())):
        num, l, r, achieve = map(int, input().split())
        k = r - l + 1
        if (k * (k + 1)) // 2 <= achieve <= (k * (num * 2 + 1 - k)) // 2:
            outpos = (r) % num
            inpos = l - 1
            ans = [0] * num
            for i in range(num, 0, -1):
                if achieve - i > 0 or (achieve - i == 0 and inpos == r - 1):
                    achieve -= i
                    ans[inpos] = i
                    inpos += 1
                else:
                    ans[outpos] = i
                    outpos += 1
                    outpos %= num
            print(*ans)
        else:
            print(-1)


# permutationbysum()

def peaks():
    for _ in range(int(input())):
        num, peak = map(int, input().split())
        pos = 1
        rpos = num
        ans = []
        now = 0
        if num == 1:
            if not peak:
                print(1)
            else:
                print(-1)
            continue
        if num == 2:
            if peak:
                print(-1)
            else:
                print(1, 2)
            continue
        added = 0
        while rpos + 1 != pos:
            if not peak:
                while pos <= rpos:
                    ans.append(pos)
                    pos += 1
                break
            if not now:
                ans.append(pos)
                pos += 1
            else:
                ans.append(rpos)
                rpos -= 1
                if num - added != 1:
                    peak -= 1
            added += 1
            now = 1 - now
        if peak:
            print(-1)
            continue
        print(*ans)


# peaks()
import sys

input = sys.stdin.readline


def addone():
    for _ in range(int(input())):
        num, changes = input().split()
        l = collections.deque(sorted([int(i) for i in num]))
        perm = collections.deque()
        changes = int(changes)
        cd = 0
        ans = len(num)
        while True:
            nextnum = l.pop()
            while perm and perm[-1] == nextnum:
                l.append(perm.pop())
            c = (10 - nextnum) - cd
            changes -= c
            cd += c
            if changes >= 0:
                if not c:
                    perm.appendleft(1 - cd)
                    l.appendleft(-cd)
                else:
                    l.appendleft(1 - cd)
                    l.appendleft(-cd)
                ans += 1
            else:
                break
        print(ans % 1000000007)


# addone()

import math


def andsequences():
    def mapping(num):
        nonlocal mnum
        nonlocal c
        num = int(num)
        if num < mnum:
            mnum = num
            c = 1
        elif num == mnum:
            c += 1
        return num

    mod = 1000000007
    for _ in range(int(input())):
        mnum = float('inf')
        c = 0
        num = int(input())
        l = list(map(mapping, input().split()))
        for i in l:
            if mnum & i != mnum:
                print(0)
                break
        else:
            if c == 1:
                print(0)
            else:
                print((math.factorial(num - 2) * (c - 1) * c) % mod)


# andsequences()

def numberdigit():
    n = ((10 ** 5) * 2)
    l = [0] * 11
    mod = 10 ** 9 + 7
    l[0] = l[1] = l[2] = l[3] = l[4] = l[5] = l[6] = l[7] = l[8] = 2
    l[9] = 3
    l[10] = 4
    for i in range(11, n):
        l.append((l[i - 10] + l[i - 9]) % mod)
    for _ in range(int(input())):
        num, c = input().split()
        c = int(c)
        ans = 0
        for i in num:
            i = int(i)
            if 10 - i > c:
                ans += 1
            else:
                ans += l[c - (10 - i)]
        print(ans % mod)


# numberdigit()

def mushroom():
    people, t1, t2, percent = map(int, input().split())
    l = []
    percent = 1 - percent * 0.01
    for i in range(1, people + 1):
        s, s1 = map(int, input().split())
        l.append([i, max(s * t1 * percent + s1 * t2, s1 * t1 * percent + s * t2)])
    l.sort(key=lambda x: (x[1]), reverse=True)
    for i in l:
        i[1] = "{:.2f}".format(i[1])
        print(*i)


# mushroom()

def escape():
    prins = int(input())
    dra = int(input())
    start = int(input())
    pack = int(input())
    c = int(input())
    speeddiff = dra - prins
    if speeddiff <= 0:
        return 0
    pd = start * prins
    ans = 0
    while pd < c:
        hs = pd / speeddiff
        pd += prins * hs
        if pd >= c:
            break
        time = pd / dra
        time += pack
        pd += prins * time
        ans += 1
    return ans


# print(escape())

def perm():
    def high(n, k):
        return k * (2 * n - k + 1) // 2

    def low(k):
        return k * (k + 1) // 2

    for _ in range(int(input())):
        num, lef, rig, s = map(int, input().split())
        k = rig - lef + 1
        rig, lef = rig - 1, lef - 1
        if not high(num, k) >= s >= low(k):
            print(-1)
            continue
        l = [0] * num
        lp = lef
        rp = lef - 1
        for i in range(num, 0, -1):
            if high(i, k) >= s and s - i >= low(k - 1) and k:
                l[lp] = i
                lp += 1
                s -= i
                k -= 1
            else:
                l[rp] = i
                rp -= 1
        if k:
            print(-1)
        else:
            print(*l)


# perm()


def newcom():
    for _ in range(int(input())):
        days, price = map(int, input().split())
        dl = input().split()
        worth = input().split()
        worth.append(0)
        ans = float('inf')
        req = 0
        left = 0
        for i in range(days):
            a = int(dl[i])
            w = int(worth[i])
            ans = min(ans, req + max(0, price - left + a - 1) // a)
            ns = max(0, w - left + a - 1) // a
            req += ns + 1
            left += a * ns - w
        print(ans)


# newcom()


def perfectsq():
    for _ in range(int(input())):
        n = input()
        for i in input().split():
            sq = math.sqrt(int(i))
            if sq != int(sq):
                print("YES")
                break
        else:
            print("NO")


# perfectsq()

def and0big():
    for _ in range(int(input())):
        l, k = map(int, input().split())
        print(l ** k % mod)


# and0big()

import math


def mod1p():
    n = int(input())
    ans = dict()
    p = 1
    for i in range(1, n):
        if math.gcd(i, n) == 1:
            ans[str(i)] = True
            p = (p * i) % n
    if p == 1:
        print(len(ans))
        print(' '.join(ans.keys()))
    else:
        ans.pop(str(p))
        print(len(ans))
        print(' '.join(ans.keys()))


# mod1p()

def shorttask():
    num = 10000100
    l = [-1] * (num + 2)
    s = [-1] * (num + 2)
    l[1] = 1
    for i in range(2, int(math.sqrt(num + 1)) + 2):
        if l[i] == -1:
            l[i] = i
            for x in range(i * i, num + 1, i):
                if l[x] == -1:
                    l[x] = i
    s[1] = 1
    for i in range(2, num + 1):
        if l[i] == -1:
            l[i] = i
            s[i] = i + 1
        else:
            i1 = i
            s[i] = 1
            while i1 % l[i] == 0:
                i1 //= l[i]
                s[i] = s[i] * l[i] + 1
            s[i] *= s[i1]
    ans = [-1] * (num + 1)
    for i in range(num, 0, -1):
        if s[i] < num:
            ans[s[i]] = i
    for _ in range(int(input())):
        print(ans[int(input())])


# shorttask()

def review():
    for _ in range(int(input())):
        n = int(input())
        ans = 0
        for i in input().split():
            i = int(i)
            if i == 1 or i == 3:
                ans += 1
        print(ans)


# review()

def GCDleng():
    po10 = [0] * 11
    po10[1] = 1
    for i in range(2, 11):
        po10[i] = po10[i - 1] * 10
    for _ in range(int(input())):
        n, n1, res = map(int, input().split())
        print(po10[n], po10[n1] + po10[res])


# GCDleng()


def anothercarddeck():
    n, q = map(int, input().split())
    l = input().split()
    d = {l[i]: i for i in range(n - 1, -1, -1)}
    ans = []
    for i in input().split():
        now = d[i]
        ans.append(now + 1)
        for key in d:
            if d[key] < now:
                d[key] += 1
        d[i] = 0
    print(*ans)


# anothercarddeck()

def mincoststring():
    n, letters = map(int, input().split())
    l = [chr(i + 97) for i in range(letters)]
    ans = []
    real = letters - 1
    if not n:
        print(*ans, sep='')
        return
    if n == 1:
        print(*ans, sep='', end='')
        print(l[1 % (real + 1)])
        return
    while n:
        for i in range(len(l)):
            for i1 in range(i, len(l)):
                if i1 != real:
                    ans.append(l[i1])
                    ans.append(l[i])
                    n -= 2
                else:
                    ans.append(l[i1])
                    n -= 1
                if not n:
                    print(*ans, sep='')
                    return
                if n == 1:
                    print(*ans, sep='', end='')
                    print(l[(i1 + 1) % (real + 1)])
                    return
    print(*ans)


# mincoststring()


def mincost2():
    n, letters = map(int, input().split())
    l = [chr(i + 97) for i in range(letters)]
    comb = []
    if letters == 1 or n == 1:
        print('a' * n)
        return
    for i in range(letters):
        for i1 in range(i, letters):
            comb.append(l[i1] + l[i])
    lc = len(comb)
    while True:
        for i in range(lc):
            if ord(comb[i][0]) - 97 == letters - 1:
                n -= 1
                print(comb[i][0], end='')
            else:
                n -= 2
                print(comb[i], end='')
            if n == 1:
                pos = ord(comb[i][0]) - 97 + 1
                print(l[pos % letters])
                return
            if not n:
                return


# mincost2()
def Tittat():
    for _ in range(int(input())):
        n, k = map(int, input().split())
        l = list(map(int, input().split()))
        for i in range(n):
            if not k:
                break
            while k and l[i]:
                l[i] -= 1
                l[-1] += 1
                k -= 1
        print(*l)


# Tittat()

def xorq2():
    for _ in range(int(input())):
        n = int(input())
        s = 0
        num = -1
        nc = 0
        c = 0
        for i in input().split():
            i = int(i)
            s ^= i
            c += 1
            if num == -1 and s == i:
                num = s
                s = 0
                nc += c
                c = 0
            if num != -1 and (s == num or not s):
                s = 0
                nc += c
                c = 0
        print(['NO', 'YES'][nc == n])


# xorq2()


def xorq2re():
    n = int(input())
    s = input().split()
    xor = 0
    for i in range(n):
        s[i] = int(s[i])
        xor ^= s[i]
    if not xor:
        print("YES")
    else:
        new = 0
        ans = 0
        for i in s:
            new ^= i
            if new == xor:
                new = 0
                ans += 1
        print(["NO", "YES"][ans > 1])


import sys

sys.setrecursionlimit(2300)


def q3partition():
    def partition():
        # if tol - now == now:
        #     return True
        # return (partition(l[pos] + now, pos + 1) or partition(now, pos + 1)) if pos < n and now <= tol else False
        if tol % 2:
            return 0
        up = tol * 2
        rec = [[False] * (up + 10) for _ in range(n + 1)]
        rec[0][tol] = True
        for i in range(1, n + 1):
            v = l[i - 1]
            for j in range(up + 1):
                if rec[i - 1][j]:
                    if v + j <= up + 3:
                        rec[i][j + v] = True
                    if j >= v:
                        rec[i][j - v] = True
        return rec[n][tol]

    def ints(x):
        nonlocal tol
        x = int(x)
        tol += x
        return x

    n = int(input())
    tol = 0
    l = list(map(ints, input().split()))
    if partition():
        gcf = reduce(lambda x, y: math.gcd(x, y), l)
        pos = 1
        for i in l:
            if i // gcf % 2:
                print(1)
                print(pos)
                return
            pos += 1
    else:
        print(0)


def main():
    # for _ in range(int(input())):
    q3partition()


main()

```