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.buffer.readline

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

if __name__ == "__main__":
    main()