#include <bits/stdc++.h>
#define int long long
#define range(i, a, b) for(auto i = a; i < b; i++)
#define rep(i, a) range(i, 0, a)
using namespace std;
const int INF = sizeof(int) == sizeof(long long) ? 1000000000000000000LL : 1000000000;
const int MOD = 1000000007;
const long double EPS = 1e-8;

signed main() {
	int n;
	cin >> n;
	int a[n];
	int sum = 1;
	vector <int> s;
	int pear = -1, berry = -1;
	rep (i, n) {
		cin >> a[i];
		if (abs(a[i]) == 2) {
			sum *= a[i];
			s.push_back(i + 1);
		}
		if (a[i] == -1 && pear == -1) pear = i + 1;
		if (a[i] == -2) berry = s.size() - 1;
	}
	if (sum == 1) {
		cout << 0 << endl;
	} else if (sum > 0 ) {
		cout << s.size() << endl;
		rep (i, s.size()) cout << s[i] << endl;
	} else if (pear != -1) {
		s.push_back(pear);
		sort(s.begin(), s.end());
		cout << s.size() << endl;
		rep (i, s.size()) cout << s[i] << endl;
	} else {
		cout << s.size() - 1 << endl;
		rep (i, s.size()) if (i != berry) cout << s[i] << endl;
	}
	return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

B： 階層的計算機 (Hierarchical Calculator)

Problem

Ebi-chan has N formulae: y = a_i x for i =1, ..., N (inclusive). Now she considers a subsequence of indices with length k: s_1, s_2, ..., s_k. At first, let x_0 be 1 and evaluate s_1-th formulae with x = x_0. Next, let x_1 be the output of s_1 and evaluate s_2-th formulae with x = x_1, and so on.

She wants to maximize the final output of the procedure, x_{s_k}. If there are many candidates, she wants the """shortest one""". If there are still many candidates, she wants the """lexicographically smallest one""".

Sequence s is lexicographically smaller than sequence t, if and only if either of the following conditions hold:

* there exists m < |s| such that s_i = t_i for i in 1 to m (inclusive) and s_{m+1} < t_{m+1}, or
* s_i = t_i for i in 1 to |s| (inclusive) and |s| < |t|,



where |s| is the length of the s.

Input


N
a_1 a_2 $\cdots$ a_N


Constraints

* 1 \leq N \leq 60
* -2 \leq a_i \leq 2 for i=1, ...,N (inclusive)
* Every input is given as the integer.



Output

Output k+1 lines. First line, the length of the sequence, k. Following k lines, the index of the i-th element of the subsequence, s_i (one element per line).

Sample Input 1


4
2 0 -2 1


Sample Output for Input 1


1
1


She evaluates the first one and gets the maximum value 2.

Sample Input 2


3
2 -2 -2


Sample Output for Input 2


3
1
2
3


She evaluates all of them and gets the maximum value 8.

Sample Input 3


2
-1 0


Sample Output for Input 3


0

She evaluates none of them and gets the maximum value 0. Empty sequence is the shorter and lexicographically smaller than any other sequences.

Sample Input 4


5
-1 2 1 -2 -1


Sample Output for Input 4


3
1
2
4


She evaluates $\langle$ 1, 2, 4 $\rangle$ ones and gets the maximum value 4. Note that $\langle$ 2, 4, 5 $\rangle$ is not lexicographically smallest one.





Example

Input

4
2 0 -2 1


Output

1
1

### Response

```cpp
#include <bits/stdc++.h>
#define int long long
#define range(i, a, b) for(auto i = a; i < b; i++)
#define rep(i, a) range(i, 0, a)
using namespace std;
const int INF = sizeof(int) == sizeof(long long) ? 1000000000000000000LL : 1000000000;
const int MOD = 1000000007;
const long double EPS = 1e-8;

signed main() {
	int n;
	cin >> n;
	int a[n];
	int sum = 1;
	vector <int> s;
	int pear = -1, berry = -1;
	rep (i, n) {
		cin >> a[i];
		if (abs(a[i]) == 2) {
			sum *= a[i];
			s.push_back(i + 1);
		}
		if (a[i] == -1 && pear == -1) pear = i + 1;
		if (a[i] == -2) berry = s.size() - 1;
	}
	if (sum == 1) {
		cout << 0 << endl;
	} else if (sum > 0 ) {
		cout << s.size() << endl;
		rep (i, s.size()) cout << s[i] << endl;
	} else if (pear != -1) {
		s.push_back(pear);
		sort(s.begin(), s.end());
		cout << s.size() << endl;
		rep (i, s.size()) cout << s[i] << endl;
	} else {
		cout << s.size() - 1 << endl;
		rep (i, s.size()) if (i != berry) cout << s[i] << endl;
	}
	return 0;
}

```