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:
ss = input()
n = len(ss)

if ss[0] == '0' or ss[-1] == '1':
    print(-1)
    exit()
else:
    for s1, s2 in zip(ss[:n//2], ss[n//2-1:-1][::-1]):
#        print(s1, s2)
        if s1 != s2:
            print(-1)
            exit()

vMin, vMax = 1, n
iPrev = 0
#for i, s in enumerate(ss[:n//2], 1):
for i, s in enumerate(ss, 1):
    if s == '0': continue
#    print(i, ':', vMin)
#    if vMin > 1:
    print(vMin, vMin + 1)

    for j in range(i - iPrev - 1):
        print(vMin, vMax)
        vMax -= 1

    vMin += 1
    iPrev = i