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 = list(input())\nn = len(s)\nif s[n - 1] == "1" or s[0] == "0":\n    print(-1)\n    return\nfor i in range((n - 1) // 2):\n    if not s[i] == s[n - 2 - i]:\n        print(-1)\n        return\nl = n - s.count("0") + 1\nx = [0] * l\nj = 0\nfor i in range(n // 2):\n    if s[i] == "1":\n        j += 1\n    else:\n        x[j] += 1\n        x[l - 1 - j] += 1\n        if j == l - 1 - j and n % 2 == 0 and i == (n - 1) // 2:\n            x[j] -= 1\nfor i in range(l - 1):\n    print(i + 1, i + 2)\nk = n - s.count("0") + 2\nfor i in range(l):\n    for _ in range(x[i]):\n        print(i + 1, k)\n        k += 1'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: