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 = 'import sys\n\nini = lambda: int(sys.stdin.readline())\ninl = lambda: [int(x) for x in sys.stdin.readline().split()]\nins = lambda: sys.stdin.readline().rstrip()\ndebug = lambda *a, **kw: print("\\033[33m", *a, "\\033[0m", **dict(file=sys.stderr, **kw))\n\n\nclass Node:\n    def __init__(self, val):\n        self.val = val\n        self.par = None\n\n\ndef solve():\n    s = [x == "1" for x in ins()]\n    n = len(s)\n    if s[-1]:\n        return print(-1)\n    for i in range(n - 1):\n        if s[i] != s[n - 2 - i]:\n            return print(-1)\n    if not s[0]:\n        return print(-1)\n\n    h = (n + 1) // 2\n    nodes = [Node(i) for i in range(n)]\n    for i in range(1, n):\n        nodes[i].par = nodes[i - 1]\n\n    i = 1\n    while i + 2 < n:\n        if s[i]:\n            i += 1\n            continue\n        nodes[i + 2].par = nodes[i]\n        nodes[i], nodes[i + 1] = nodes[i + 1], nodes[i]\n        i += 1\n\n    edges = set()\n    for i in range(1, n):\n        u = nodes[i].val\n        v = nodes[i].par.val\n        edges.add((min(u, v) + 1, max(u, v) + 1))\n    for u, v in edges:\n        print(u, v)\n\n\nsolve()\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 18047