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(10**6)

s = input().rstrip()
N = len(s)
if s[0] == '0' or s[-1] == '1' or s[:-1] != s[:-1][::-1]:
    print(-1)
    exit()
subtree = [[] for _ in range(N+1)]
prev = 1
for i in range(2, N+1):
    if s[i-1] == '1' or i == N:
        subtree[i] = [prev] + [1] * (i-prev-1)
        prev = i

i = 1
def dfs(size):
    global i
    v = i
    for c in subtree[size]:
        i += 1
        print(v, i)
        dfs(c)

dfs(N)