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: Accepted)

#include <bits/stdc++.h>
#define ll long long int
#define mp make_pair
#define pb push_back
#define ff first 
#define ss second
#define mod 1000000007
#define lim 100005
#define nfs_mw ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
using namespace std;

int rsz[lim] = {};

int main()
{
	// nfs_mw;
	int i,u,n; string s;
	cin>>s;
	n = s.size();

	if((s[0] == '0') || (s[n-1] == '1')){
		cout<<(-1)<<"\n";
		return 0;
	}

	for(i=0; i<n/2; i++) if(s[i] != s[n-i-2]) {
		cout<<(-1)<<"\n";
		return 0;
	}

	rsz[u = 1] = n - 1;

	for(i=(n/2); i; i--)
		if(s[i-1] == '1'){
			rsz[u] -= i;
			cout<<u<<" "<<(u+1)<<"\n";
			rsz[++u] = i-1;
		}

	for(i=u; i; i--)
		while(rsz[i]--)
			cout<<i<<" "<<(++u)<<"\n";		
}