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 = input()
N = len(S)

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

mem = []
for i in range(N//2):
    if S[i] != S[-2-i]:
        print(-1)
        exit()
    if S[i] == '1':
        mem.append(i)

if len(mem)==0:
    print(-1)
    exit()

ans = []
for i in range(1,len(mem)+1):
    ans.append((i,i+1))

last_v = len(mem)+1

for i in range(mem[0]):
    last_v += 1
    ans.append((1,last_v))

for i,(a,b) in enumerate(zip(mem, mem[1:])):
    n = i+2
    k = b-a-1
    for _ in range(k):
        last_v += 1
        ans.append((n,last_v))

n = len(mem)+1
for _ in range(N):
    last_v += 1
    if last_v > N: break
    ans.append((n,last_v))

for row in ans:
    print(*row)