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;
int n;
const int maxn=1e5+10;
int vis[maxn];
pair<int,int> ans[maxn];
void dfs(int a,int b)
{
	if (a==0)return ;
	printf("%d %d\n",a,b);
	if (vis[a])dfs(a-1,a);
	else dfs(a-1,b);
}
int main()
{
	int n=0;
	int x;
	while (~scanf("%1d",&x)){
		n++;
		vis[n]=x;
	}
	for (int i=0;i<=n;i++)if (vis[i]!=vis[n-i])return 0*puts("-1");
	if (vis[1]==0)return 0*puts("-1");
	dfs(n-1,n);
}