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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>


int main(){
	int N, i, j;
	char *s = (char *)malloc(sizeof(char) * 100001);
	scanf("%s", s);
	for(N = 0; s[N] != '\0'; N++);
	if(s[0] == '0' || s[N - 2] == '0' || s[N - 1] == '1'){
		printf("-1\n");
		return 0;
	}
	for(i = 0; i < N - 1; i++){
		if(s[i] != s[N - 2 - i]){
			printf("-1\n");
			return 0;
		}
	}
	int *t = (int *)malloc(sizeof(int) * N);
	for(i = 0; i < N; i++){
		t[i] = 0;
	}
	int *a = (int *)malloc(sizeof(int) * N);
	for(i = 0, j = 0; i <= N / 2; i++){
		if(s[i] == '1'){
			a[j] = i;
			j++;
			t[i] = 1;
		}
	}
	for(i = 1; i < j; i++){
		printf("%d %d\n", a[i - 1] + 1, a[i] + 1);
	}
	int *next = (int *)malloc(sizeof(int) * N);
	next[N - 1] = a[j - 1];
	for(i = N - 2; i >= 0; i--){
		if(t[i] == 1){
			next[i] = i;
		}
		else{
			next[i] = next[i + 1];
		}
	}
	for(i = 0; i < N; i++){
		if(t[i] == 0){
			printf("%d %d\n", i + 1, next[i] + 1);
		}
	}
	return 0;
}