Problem: 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.

Examples

Input

1111


Output

-1


Input

1110


Output

1 2
2 3
3 4


Input

1010


Output

1 2
1 3
1 4

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;

const int MAXN = 100010;

char s[MAXN];
int n, fa[MAXN];

int main()
{
	scanf("%s", s + 1); n = strlen(s + 1);
	if(s[1] != '1' || s[n] != '0') return puts("-1"), 0;
	for(int i = 1; i <= n / 2; ++i)
		if(s[i] != s[n - i]) return puts("-1"), 0;
	int rt = 1, now = 1;
	for(int i = 2; i <= n; ++i)
		if(s[i] == '1')
		{
			now = i;
			for(int j = rt; j < now; ++j)
				printf("%d %d\n", j, now);
			rt = now;
		}
	printf("%d %d\n", n - 1, n);
	return 0;
}