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: Wrong Answer)

#include <algorithm>
#include <iostream>
#include <iomanip>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <list>
#include <cmath>
#include <stack>
#include <string>
#include <cstring>
#include <numeric>
const int inf=1e9+7;
const int mod=1e9+7;
using namespace std;
//
int main(){
	string s;
	cin>>s;
	int N=s.size();
	vector<char> S;
	S.push_back('0');
	for(int i=0;i<N;i++){
		S.push_back(s[i]);
	}
	for(int i=0;i<N;i++){
		if(S[i]!=S[N-i]){
			cout<<-1<<endl;
			return 0;
		}
	}
	vector<pair<int,int>> E;
	for(int i=1;i<N;i++){
		E.push_back(make_pair(i,i+1));
	}
	for(int i=2;i<N/2;i++){
		if(S[i]=='0'){
			E[i-2].second=i+1;
		}
	}
	for(int i=0;i<N-1;i++){
		cout<<E[i].first<<" "<<E[i].second<<endl;;
	}
	return 0;
}