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<bits/stdc++.h>
using namespace std;
const int maxn=110000;
vector<int> oa,ob;
int n;
char s[maxn];
int fa[maxn];
int check()
{
	if(s[n]=='1') return 0;
	for(int i=1;i<=n-1;i++) 
	{
		if(s[i]==s[n-i]) continue;
		return 0;
	}
	if(s[1]=='0') return 0;
	return 1;
}
int main()
{
	scanf("%s",s+1);
	n=strlen(s+1);
	if(!check()) return printf("-1\n"),0;
	for(int i=1;i<=n;i++) fa[i]=i;
	for(int i=n-1;i>=1;i--) 
	{
		if(s[i]=='0') fa[i]=fa[i+1];
		else fa[i]=i+1;
	}
	for(int i=1;i<=n;i++)
	{
		if(fa[i]==i) continue;
		printf("%d %d\n",i,fa[i]);
	}
	return 0;
}