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 PYTHON3):

Solution:
import sys
input = sys.stdin.readline
sys.setrecursionlimit(pow(10, 6))
from collections import deque

def main():
    s = input().strip()
    if s[-1] == '1' or s[0] == '0':
        print(-1)
    else:
        edges = deque([])
        for i in range(len(s)-1):
            if s[i] != s[len(s)-i-2]:
                print(-1)
                return
            elif s[i] == '1':
                edges.append(i)
        edges.append(len(s)-1)
        for i in range(len(s)-1):
            if edges[0] == i:
                edges.popleft()
            print(i+1, edges[0]+1)


if __name__ == '__main__':
    main()