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
def LI2(): return list(map(int,sys.stdin.readline().rstrip()))  #空白なし


S = LI2()
n = len(S)

if S[-1] == 1 or S[0] == 0 or S[-2] == 0:
    print(-1)
    exit()

for i in range(n-1):
    if S[i] != S[-2-i]:
        print(-1)
        exit()


k = S.count(1)  # 1の個数
for i in range(k):
    print(i+1,i+2)

a = 1  # 付け足す辺の端点
b = k+2  # 付け足す頂点のindex
for i in range(n-1):
    if S[i] == 1:
        a += 1
    else:
        print(a,b)
        b += 1