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(map(int, input()))\nn = len(s)\nif s[0]==0 or s[-1] == 1 or any(s[i]!=s[i] for i in range(n//2)):\n    print((-1))\n    return\nG = [[] for i in range(n)]\ncur = 0\nfor i in range(n-1):\n    G[cur].append(i+1)\n    G[i+1].append(cur)\n\n    if s[i]:\n        cur = i+1\n\nroot = n//2\nfrom collections import deque\nsize = [1]*n\nans = [0]*n\nedges = []\ndef bfs1(root):\n    rev = [(root, -1)]\n    for i in range(n):\n        cur, par = rev[i]\n        for to in G[cur]:\n            if to != par:\n                rev.append((to, cur))\n    for i in reversed(list(range(1,n))):\n        cur, par = rev[i]\n        size[par] += size[cur]\n        ans[size[cur]] = 1\n        ans[n-size[cur]] = 1\n        edges.append([cur+1, par+1])\nbfs1(0)\n\nif any(ans[i+1]!=s[i] for i in range(n-1)):\n    print((-1))\n    return\n\nfor i in edges:\n    print((*i))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: