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(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]

def ng():
    if s[0]=="0" or s[-1]=="1":return True
    for i in range(n):
        if i>n-2-i:break
        if s[i]!=s[n-2-i]:return True
    return False

s=SI()
n=len(s)

if ng():
    print(-1)
    exit()

aa=[]
for i in range(n//2):
    if s[i]=="1":aa.append(i+1)
aa.append(n)

ans=[]
for i in range(len(aa)-1):ans.append([i+1,i+2])

j=len(aa)+1
for i,(a0,a1) in enumerate(zip(aa,aa[1:])):
    for _ in range(a1-a0-1):
        ans.append([i+2,j])
        j+=1

for u,v in ans:print(u,v)