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:
from sys import exit
def muri():
    print(-1)
    exit()

L = list(map(int, input()))
N = len(L)
if L.pop():
    muri()
if not L[0]:
    muri()
if L != L[::-1]:
    muri()
if N == 2:
    print(1, 2)
    exit()

Ans = []
M = [i for i, l in enumerate(L, 1) if l] 
K = [0] + [m2 - m1 - 1 for m1, m2 in zip(M, M[1:])] + [0]
p = 1
for _ in range(len(M)):
    Ans.append((p, p+1))
    p += 1
p += 1
for j, k in enumerate(K, 1):
    for _ in range(k):
        Ans.append((j, p))
        p += 1

for a in Ans:
    print(*a)