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:
s = input()
n = len(s)

if s[0] == '0' or s[-1] == '1':
    print(-1)
    exit()
for i in range(n-1):
    if s[i] != s[-2-i]:
        print(-1)
        exit()

path = {1:[v for v in range(2, n+1)]}

ans = []
u_cur, v_cur = 1, 2
n_prev = 0
for i in range(1, n//2):
    if s[i] == '1':
        for _ in range(i-n_prev):
            ans.append((u_cur, v_cur))
            v_cur += 1
        ans.append((v_cur, u_cur))
        u_cur, v_cur = v_cur, v_cur+1
        n_prev = i+1
for v in range(v_cur, n+1):
    ans.append((v_cur-1, v))
for a in ans:
    print(*a)