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.

-----Sample Input-----
1111

-----Sample Output-----
-1

It is impossible to have a connected component of size n after removing one edge from a tree with n vertices.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 's = input()\nif s[0] == "0" or s[-1] == "1":\n    print((-1))\n    return\nn = len(s)\nif n == 2:\n    if s == "10":\n        print((1, 2))\n        return\n    else:\n        print((-1))\n        return\n\nm = n // 2\ntmp = m + 1\nANS = []\nfor i in reversed(list(range(1, m + 1))):\n    j = n - i\n    if s[i - 1] == "1" and s[j - 1] == "1":\n        ANS.append((tmp, i))\n        tmp = i\n    elif s[i - 1] == "0" and s[j - 1] == "0":\n        ANS.append((tmp, i))\n    else:\n        print((-1))\n        return\nfor i in range(m + 2, n + 1):\n    ANS.append((m + 1, i))\n\nfor a, b in ANS:\n    print((a, b))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: