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>
#define ll long long
using namespace std;
int n,m,cnt,la,a[200010][2],rt;
char s[200010];
void build(int x,int y){
	a[++cnt][0]=x;a[cnt][1]=y;
}
int main(){
	int i,j;
	scanf("%s",s+1);
	n=strlen(s+1);
	for(i=1;i<n;i++)if(s[i]!=s[n-i])return puts("-1"),0;
	if(s[1]=='0'||s[n]=='1')return puts("-1"),0;
	m=1;rt=1;la=1;
	for(i=2;i<=n;i++)if(s[i]=='1'){
		build(rt,++m);rt=m;
		for(j=1;j<i-la;j++)build(rt,++m);la=i;
	}
	build(rt,++m);
	rt=m;
	for(i=m+1;i<=n;i++)build(rt,i);
	for(i=1;i<n;i++)printf("%d %d\n",a[i][0],a[i][1]);
}