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()

cnt = 0
# サイズnの連結成分は必ず作れない
# サイズ1の連結成分は必ず作れる
if s[-1] == "1" or s[0] == "0":
    print(-1)
    exit()
    
li = []
for i in range(1, len(s) // 2):
    if s[i] != s[-i-2]:
        print(-1)
        exit()
    if s[i] == "1":
        li.append(i + 1)
        
tree = []
j = 1
for _ in range(len(li)):
    tree.append((j, j + 1))
    j += 1
li.append(len(s))

cnt = 0
for i in range(len(li)):
    cnt += 1
    while cnt < li[i]:
        tree.append((i + 1, j + 1))
        j += 1
        cnt += 1

for edge in tree:
    print(*edge)