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()

num = len(s)

if s[-1] == "1" or s[0] == "0":
    print (-1)
    sys.exit()

s = s[:-1]

for i in range(num // 2):
    
    if s[i] != s[-1-i]:
        print (-1)
        sys.exit()

lis = []
ans = []

for i in range(num-1):

    if i != 0 and s[i] == "1":
        lis.append(i+1)

#print (lis)

now = 1
for i in range(len(lis)):

    while now < lis[i]:
        ans.append([now,lis[i]])
        now += 1

    if i != len(lis)-1:
        ans.append([lis[i],lis[i+1]])
        now += 1

ans.append([num-1,num])


for i in ans:
    print (i[0],i[1])