Consider a pyramid made up of blocks. Each layer of the pyramid is a rectangle of blocks, and the dimensions of these rectangles increment as you descend the pyramid. So, if a layer is a `3x6` rectangle of blocks, then the next layer will be a `4x7` rectangle of blocks. A `1x10` layer will be on top of a `2x11` layer on top of a `3x12` layer, and so on.

## Task

Given the dimensions of a pyramid's topmost layer `w,l`, and its height `h` (aka the number of layers), return the total number of blocks in the pyramid.

## Examples

`num_blocks(1, 1, 2)` will return `5`. This pyramid starts with a `1x1` layer and has 2 layers total. So, there is 1 block in the first layer, and `2x2=4` blocks in the second. Thus, 5 is the total number of blocks.

`num_blocks(2, 4, 3)` will return `47`. This pyramid has 3 layers: `2x4`, `3x5`, and `4x6`. So, there are `47` blocks total.

## Notes

All parameters will always be postive nonzero integers.

Efficiency is important. There will be:

* 100 'small' cases with `w`, `l`, and `h` below `20`.
* 100 'big' cases with `w`, `l`, and `h` between `1e9` and `1e10`.

```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 num_blocks (width, length, height):\n    \n    def linsum (n):\n        return n * (n+1) // 2\n        \n    def sqrsum (n):\n        return n * (n+1) * (2*n+1) // 6\n        \n    cube = width * length * height\n    stairs = (width+length) * linsum(height-1)\n    corner = sqrsum(height-1)\n    \n    return cube + stairs + corner\n    \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'num_blocks'
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: 5504