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
S = input()
N = len(S)
ss = S[:N-1]
if S[-1] == '1' or ss != ss[::-1] or S[0] == '0':
    print(-1)
    sys.exit()
tree = []
cnt = 0
for s in ss:
    if s == '1':
        tree.append(cnt)
        cnt = 0
    else:
        cnt += 1
ans = []
now = 1
for c in tree:
    for i in range(c):
        ans.append((now, now+i+1))
    ans.append((now, now+c+1))
    now = now+c+1
for a, b in ans:
    print(a, b)