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 os
import sys

if os.getenv("LOCAL"):
    sys.stdin = open("_in.txt", "r")

sys.setrecursionlimit(2147483647)
INF = float("inf")
IINF = 10 ** 18
MOD = 10 ** 9 + 7

S = sys.stdin.readline().rstrip()


def solve(S: str):
    if S[-1] == '1':
        return None
    S = S[:-1]
    if S[::-1] != S:
        return None
    if S[0] == '0':
        return None
    ret = [(1, 2)]
    v = 2
    for i in range(1, (len(S) + 1) // 2):
        ret.append((v, i + 2))
        if S[i] == '1':
            v = i + 2
    for i in range((len(S) + 1) // 2, len(S)):
        ret.append((v, i + 2))

    return ret


ans = solve(S)
if ans:
    for r in ans:
        print(*r)
else:
    print(-1)