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;
int n, can[100010];
char str[100010];
int main()
{
	scanf(" %s", str);
	n = strlen(str);
	for (int i = 1; i <= n; i++)
	{
		char a = str[i-1];
		if (a == '1') can[i] = 1;
	}
	for (int i = 1; i <= n; i++)
	{
		if (can[i] && !can[n-i])
		{
			printf("-1\n");
			return 0;
		}
	}
	if (!can[1])
	{
		printf("-1\n");
		return 0;
	}
	int upto = 0;
	int node = 0;
	int children = 0;
	for (int i = 2; i <= n/2; i++)
	{
		if (can[i])
		{
			++upto;
			if (node != 0)
			{
				printf("%d %d\n", node, upto);
			}
			node = upto;
			while (children < i)
			{
				upto++;
				printf("%d %d\n", node, upto);
				children++;
			}
		}
	}
	if (upto != n)
	{
		upto++;
		if (node != 0) printf("%d %d\n", upto, node);
		node = upto;
		while (upto < n) printf("%d %d\n", node, ++upto);
	}
	// Make the tree
}