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<cstdio>
#include<cstring>
using namespace std;
int n,now;
char s[100010];
int main() {
	scanf("%s",s+1); n=strlen(s+1);
	if (s[n]=='1') {
		printf("-1\n"); return 0;
	}
	if (s[1]=='0') {
		printf("-1\n"); return 0;
	}
	for (int i=1,j=n-1;i<n;i++,j--) if (s[i]!=s[j]) {
		printf("-1\n"); return 0;
	}
	now=1;
	for (int i=2;i*2<=n;i++) {
		if (s[i]=='1') {
			printf("%d %d\n",now,i);
			for (int j=now+1;j<i;j++) printf("%d %d\n",i,j);
			now=i;
		}
	}
	for (int i=now;i<n;i++) printf("%d %d\n",i,n);
	return 0;
}