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()
slen=len(s)-1
slen2=(len(s)-1)//2
iswitch=0
for i in range(slen2):
    if s[i]!=s[slen-i-1]:
        iswitch=1

if s[-1]=='1' or s[0]=='0':
    iswitch=1

if iswitch==1:
    print(-1)
else:
    if slen==1:
        print("1 1")
    elif slen==2:
        print("1 2")
        print("1 3")
    else:
        if True:
            henlist=[]
            mae=1
            jswitch=0
            for i in range(slen):
                now=i+2
                if jswitch==0:
                    if s[now-1]=='1':
                        for i in range(now-mae):
                            henlist.append([mae+i, now])
                        mae=now
                        if now>(len(s))//2:
                            jswitch=1
                    else:
                        pass
                else:
                    henlist.append([mae, now])
        for hl in henlist:
            print(hl[0], hl[1])