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 PYTHON):

Solution:
#!/usr/bin/python
# -*- coding: utf-8 -*-
import sys,collections,itertools,re,math,fractions,decimal,random,array,bisect,heapq

# decimal.getcontext().prec = 50
# sys.setrecursionlimit(10000)
# MOD = 10**9 + 7

def solve(f):
    s = f.read_str()
    n = len(s)
    a = map(int, list(s))

    if a[-1] == 1: return -1
    if a[0] == 0: return -1

    va = [n]
    for i in xrange(n/2):
        if a[i] != a[-i-2]: return -1
        if a[i] == 1:
            vv = va.pop()
            va.extend([vv-(n-(i+1)), n-(i+1)])

    ans = ["%d %d"%(i+1, i+2) for i in xrange(len(va)-1)]
    c = len(va) + 1
    for i, v in enumerate(va):
        for _ in xrange(v-1):
            ans.append("%d %d"%(i+1, c))
            c += 1

    return "\n".join(ans)


class Reader(object):
    def __init__(self, filename=None):
        self.file = open(filename) if filename is not None else None
        self.case = 1

    def __readline(self):
        return self.file.next().strip() if self.file else raw_input()

    def next_case(self):
        self.file.next()
        self.case += 1

    def read_int(self): return int(self.__readline())
    def read_float(self): return float(self.__readline())
    def read_long(self): return long(self.__readline())
    def read_decimal(self): return decimal.Decimal(self.__readline())
    def read_str(self): return self.__readline()

    def read_int_list(self): return map(int, self.__readline().split())
    def read_float_list(self): return map(float, self.__readline().split())
    def read_long_list(self): return map(long, self.__readline().split())
    def read_decimal_list(self): return map(decimal.Decimal, self.__readline().split())
    def read_str_list(self): return self.__readline().split()

if __name__ == '__main__':
    filename = sys.argv[1] if len(sys.argv) > 1 else None
    f = Reader(filename)
    if f.file:
        while True:
            print "Case #%d\n"%f.case, solve(f)
            try:
                f.next_case()
            except StopIteration:
                break
    else:
        print solve(f)