Imagine a funnel filled with letters. The bottom letter drops out of the funnel and onto a conveyor belt:

```
  \b,c/  -->   \b,c/
   \a/   -->    \ /
                 a
-------     -------
```
If there are two letters above a gap, the smaller letter falls into the gap.
```
  \b,c/   -->   \  c/ 
   \ /    -->    \b/   
a            a         
-------      -------
```
Of course, this can create a new gap, which must also be filled in the same way:
```
  \f,e,d/  -->  \f, ,d/
   \  c/   -->   \e,c/ 
    \b/           \b/   
   a            a         
  -------      -------
```
Once all the gaps above it have been filled, the bottom letter drops out of the funnel and onto the conveyorbelt. The process continues until all letters have fallen onto the conveyor. (New letters fall onto the end of the existing string)

**KATA GOAL: Return the string on the conveyorbelt after all letters have fallen**.
```
\f, ,d/      \f, ,d/   --> etc -->    \     /
 \e,c/        \e,c/    --> etc -->     \   /
  \b/    -->   \ /     --> etc -->      \ /
a           a   b                   abcdef
-------     -------                 -------
```
All letters in the funnel will be unique i.e. in every comparison one letter will be strictly smaller than the other. The funnel will be presented as a nested list, e.g:
```
[["d","a","c"],
   ["b","e"],
     ["f"]]
```
The value of a letter is defined by its codepoint. Note: this means all capital letters are defined as smaller than all lower-case letters, but your language's comparison operator will probably treat it that way automatically.

The funnels will always be "nice" -- every layer will have 1 item more than the layer below, and every layer will be full, and generally there's no funny business or surprises to consider. The only characters used are standard uppercase and lowercase letters A-Z and a-z. The tests go up to 9 layer funnel.

### Fully Worked Example
```
\d,a,c/      \d,a,c/      \d,a,c/ -->  \d   c/     
 \b,e/        \b,e/  -->   \  e/  -->   \a,e/
  \f/   -->    \ /   -->    \b/          \b/  --> 
                f        f            f
------      -------      -------      -------


\d   c/      \d   c/ -->  \    c/      \    c/     
 \a,e/  -->   \  e/  -->   \d,e/        \d,e/  -->
  \ /   -->    \a/          \a/   -->    \ /   -->
f  b        fb           fb           fb  a
------      -------      -------      -------


 \    c/      \    c/      \    c/ -->  \     /     
  \  e/        \  e/  -->   \   /  -->   \  c/   
   \d/   -->    \ /   -->    \e/          \e/  -->
fba          fba d       fbad          fbad
-------      -------     --------      -------


  \     /      \     /      \     /
   \  c/  -->   \   /        \   / 
    \ /          \c/   -->    \ /   
fbad e       fbade        fbadec         
-------      -------      -------

DONE. Return "fbadec".

```

**For a bigger funneling challenge, check out [this kata](https://www.codewars.com/kata/create-a-funnel) by @myjinxin2015.**

```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

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def funnel_out(funnel):\n    break_outs, n = [], len(funnel)\n    while len(break_outs) < n*(n+1)/2:\n        break_outs.append(funnel[-1][0])\n        funnel[-1][0], prev = \'~\', 0\n        for i in range(len(funnel) - 1, 0, -1):\n            m = min(funnel[i-1][prev:prev+2])\n            index = funnel[i-1].index(m)\n            funnel[i-1][index], funnel[i][prev], prev = \'~\', m, index\n    return "".join(break_outs)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'funnel_out'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5826