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
sys.setrecursionlimit(10000000)
MOD = 10 ** 9 + 7
INF = 10 ** 15

def main():
    S = input()
    N = len(S)
    if S[0] == '0' or S[-1] == '1':
        print(-1)
        return
    cnt = 0
    flag = True
    for i in range(N - 1):
        if S[i] != S[N - i - 2]:
            flag = False
            break
        if S[i] == '1':
            cnt += 1
    if not flag:
        print(-1)
        return
    
    edge = []
    for i in range(cnt):
        edge.append((i + 1,i + 2))
    
    extend = 0
    now = cnt + 2
    vertex = 2
    for i in range(1,N - 1):
        if S[i] == '0':
            extend += 1
        else:
            for _ in range(extend):
                edge.append((vertex,now))
                now += 1
            extend = 0
            vertex += 1

    if now == N + 1:
        print('\n'.join(' '.join(map(str,a)) for a in edge))
    else:
        print(-1)
if __name__ == '__main__':
    main()