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 = list(map(int, input()))
n = len(s)
if s[0]==0 or s[-1] == 1 or any(s[i]!=s[i] for i in range(n//2)):
    print(-1)
    exit()
G = [[] for i in range(n)]
cur = 0
for i in range(n-1):
    G[cur].append(i+1)
    G[i+1].append(cur)

    if s[i]:
        cur = i+1

root = n//2
from collections import deque
size = [1]*n
ans = [0]*n
edges = []
def bfs1(root):
    rev = [(root, -1)]
    for i in range(n):
        cur, par = rev[i]
        for to in G[cur]:
            if to != par:
                rev.append((to, cur))
    for i in reversed(range(1,n)):
        cur, par = rev[i]
        size[par] += size[cur]
        ans[size[cur]] = 1
        ans[n-size[cur]] = 1
        edges.append([cur+1, par+1])
bfs1(0)

if any(ans[i+1]!=s[i] for i in range(n-1)):
    print(-1)
    exit()

for i in edges:
    print(*i)