Problem:
Score : 700 points

Problem Statement

You are given a string s of length n.
Does a tree with n vertices that satisfies the following conditions exist?

The vertices are numbered 1,2,..., n.

The edges are numbered 1,2,..., n-1, and Edge i connects Vertex u_i and v_i.

If the i-th character in s is 1, we can have a connected component of size i by removing one edge from the tree.

If the i-th character in s is 0, we cannot have a connected component of size i by removing any one edge from the tree.

If such a tree exists, construct one such tree.

Constraints

2 \leq n \leq 10^5

s is a string of length n consisting of 0 and 1.

Input

Input is given from Standard Input in the following format:

s

Output

If a tree with n vertices that satisfies the conditions does not exist, print -1.

If a tree with n vertices that satisfies the conditions exist, print n-1 lines.
The i-th line should contain u_i and v_i with a space in between.
If there are multiple trees that satisfy the conditions, any such tree will be accepted.

Sample Input 1

1111

Sample Output 1

-1

It is impossible to have a connected component of size n after removing one edge from a tree with n vertices.

Sample Input 2

1110

Sample Output 2

1 2
2 3
3 4

If Edge 1 or Edge 3 is removed, we will have a connected component of size 1 and another of size 3. If Edge 2 is removed, we will have two connected components, each of size 2.

Sample Input 3

1010

Sample Output 3

1 2
1 3
1 4

Removing any edge will result in a connected component of size 1 and another of size 3.

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <iostream>
#include <algorithm>
#include <vector>
#include <map>
#include <string>
#include <math.h>
using namespace std;

typedef pair<int, int> P;
#define INF (1<<31-1)
#define ll long long



int main(){

	string s;
	cin >> s;
	int n = s.length();

	map<int,int> m;
	for (int i = 0; i < n; i++)
		m[i + 1] = s[i] - '0';

	// 必要条件
	for (int i = 1; i <= n - 1; i++){
		if (m[i] != m[n - i]){
			cout << -1 << endl;
			return 1;
		}
	}
	if (m[1] != 1){
		cout << -1 << endl;
		return 1;
	}


	int prev_root = 1;
	for (int i = 2; i <= n; i++){
		if (m[i] == 1){
			if (prev_root != i)
				cout << prev_root << " " << i << endl;
			for (int j = prev_root + 1; j < i; j++)
				cout << i << " " << j << endl;
			prev_root = i;
		}
	}
	cout << prev_root << " " << n << endl;

	return 0;
}