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)

s = list(input())
n = len(s)
if s[n - 1] == "1" or s[0] == "0":
    print(-1)
    exit()
for i in range((n - 1) // 2):
    if not s[i] == s[n - 2 - i]:
        print(-1)
        exit()
l = n - s.count("0") + 1
x = [0] * l
j = 0
for i in range(n // 2):
    if s[i] == "1":
        j += 1
    else:
        x[j] += 1
        x[l - 1 - j] += 1
        if j == l - 1 - j and n % 2 == 0:
            x[j] -= 1
for i in range(l - 1):
    print(i + 1, i + 2)
k = n - s.count("0") + 2
for i in range(l):
    for _ in range(x[i]):
        print(i + 1, k)
        k += 1