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>
#define IL inline
#define _
#define ll long long
using namespace std ;

IL int gi(){
	int data = 0 , m = 1; char ch = 0;
	while(ch!='-' && (ch<'0'||ch>'9')) ch = getchar();
	if(ch == '-'){m = 0 ; ch = getchar() ; }
	while(ch >= '0' && ch <= '9'){data = (data<<1) + (data<<3) + (ch^48) ; ch = getchar(); }
	return (m) ? data : -data ; 
}

int n,lst,lst_n,oo,fa[1000005] ; char s[1000000] ;

int main() {
	scanf("%s" , s + 1) ;
	n = strlen(s + 1) ; 
	if(s[1] == '0' || s[n] == '1') return puts("-1") , 0 ;
	++ oo ;
	lst = 1 ;
	lst_n = oo ;
	int rt = oo ; 
	for(int i = 2; i <= n / 2; i ++) {
		if(s[i] == '0') continue ;
		++ oo ;
		fa[rt] = oo ;
		if(rt) rt = oo ;
		for(int j = lst + 1; j <= i-1; j++) {
			fa[++oo] = rt ;
		}
		//cout <<"i="<<i<<": "<< oo << ": " ;
		//for(int j = 1; j <= oo; j ++) cout << fa[j] << " " ; cout << endl ;
		lst = i ; 
	}
	//cout << n << ": oo = "<<oo<<endl ;
	fa[rt] = oo + 1 ; 
	int root = ++ oo ;
	for(int j = oo + 1; j <= n; j ++) fa[j] = root ;
	for(int i = 1; i <= n; i ++)
		if(i != root) printf("%d %d\n" , i , fa[i]) ;
	return 0 ; 
}