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
using namespace std;
int now,n,la,pr,tot,a[500001],b[500001];
char s[500001];
void build(int x,int y){
	tot++;
	a[tot]=x;b[tot]=y;
}
int main(){
	int i,j;
	scanf("%s",s+1);
	n=strlen(s+1);
	if(s[1]=='0'||s[n]=='1')return puts("-1"),0;
	for(i=1;i<=n/2;i++)if(s[i]!=s[n-i])return puts("-1"),0;
	la=1;pr=1;now=2;
	build(la,la+1);
	la=2;
	for(i=2;i<=n/2;i++)if(s[i]=='1'){
		now=la;
		for(j=pr+1;j<i;j++)now++,build(la,now);
		build(la,now+1);
		la=now+1;
		pr=i;
	}
	for(i=la+1;i<=n;i++)build(la,i);
	for(i=1;i<n;i++)printf("%d %d\n",a[i],b[i]);
}