Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

1111

Sample Output 1

-1

It is impossible to have a connected component of size n after removing one edge from a tree with n vertices.

Sample Input 2

1110

Sample Output 2

1 2
2 3
3 4

If Edge 1 or Edge 3 is removed, we will have a connected component of size 1 and another of size 3. If Edge 2 is removed, we will have two connected components, each of size 2.

Sample Input 3

1010

Sample Output 3

1 2
1 3
1 4

Removing any edge will result in a connected component of size 1 and another of size 3.

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

import sys
#input = sys.stdin.buffer.readline

def main():
    s = input()
    l = len(s)
    if s[0] != "1" or s[-1] != "0":
        print(-1)
    else:
        b = True
        c = 1
        for i in range(l//2):
            if b:
                if s[i] == "0":
                    b = False
                else:
                    if s[l-i-2] == "1":
                        c = i+1
                    else:
                        print(-1)
                        exit()
            else:
                if s[i] == "1":
                    print(-1)
                    exit()
        ans = []
        for i in range(c):
            ans.append((i+1,i+2))
        for i in range(l-c-1):
            ans.append((1,l-i))
        for x,y in ans:
            print(x,y)

if __name__ == "__main__":
    main()