# Introduction


Fish are an integral part of any ecosystem. Unfortunately, fish are often seen as high maintenance. Contrary to popular belief, fish actually reduce pond maintenance as they graze on string algae and bottom feed from the pond floor. They also make very enjoyable pets, providing hours of natural entertainment.



# Task


In this Kata you are fish in a pond that needs to survive by eating other fish. You can only eat fish that are the same size or smaller than yourself. 
You must create a function called fish that takes a shoal of fish as an input string. From this you must work out how many fish you can eat and ultimately the size you will grow to.


# Rules

1.  Your size starts at 1

2.  The shoal string will contain fish integers between 0-9

3.  0 = algae and wont help you feed.

4.  The fish integer represents the size of the fish (1-9).

5.  You can only eat fish the same size or less than yourself.

6.  You can eat the fish in any order you choose to maximize your size.

7   You can and only eat each fish once.

8.  The bigger fish you eat, the faster you grow. A size 2 fish equals two size 1 fish, size 3 fish equals three size 1 fish, and so on.

9.  Your size increments by one each time you reach the amounts below.


# Increase your size
Your size will increase depending how many fish you eat and on the size of the fish.
This chart shows the amount of size 1 fish you have to eat in order to increase your size.




Current size
Amount extra needed for next size
Total size 1 fish
Increase to size


1
4
4
2


2
8
12
3


3
12
24
4


4
16
40
5


5
20
60
6


6
24
84
7


 



Please note: The chart represents fish of size 1

# Returns

Return an integer of the maximum size you could be.


# Example 1
You eat the 4 fish of size 1 (4 * 1 = 4) which increases your size to 2
Now that you are size 2 you can eat the fish that are sized 1 or 2.
You then eat the 4 fish of size 2 (4 * 2 = 8) which increases your size to 3



```python
fish("11112222") => 3
```

# Example 2

You eat the 4 fish of size 1 (4 * 1 = 4) which increases your size to 2
You then eat the remainding 8 fish of size 1 (8 * 1 = 8) which increases your size to 3

```python
fish("111111111111") => 3
```

Good luck and enjoy!

# Kata Series
If you enjoyed this, then please try one of my other Katas. Any feedback, translations and grading of beta Katas are greatly appreciated. Thank you.

 Maze Runner
 Scooby Doo Puzzle
 Driving License
 Connect 4
 Vending Machine
 Snakes and Ladders
 Mastermind
 Guess Who?
 Am I safe to drive?
 Mexican Wave
 Pigs in a Pen
 Hungry Hippos
 Plenty of Fish in the Pond
 Fruit Machine
 Car Park Escape

```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 fish(shoal):\n    size, eaten = 1, 0\n    for i in range(1, 10):\n        if size < i:\n            break\n        eaten += i * shoal.count(str(i))\n        size = max(size, int(((2 * eaten + 1) ** 0.5 - 1) / 2) + 1)\n    return size'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'fish'
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: 5552