Salmon runs a fish delivery company in Fish City. Fish City has $N$ vertical roads numbered $1, 2, ..., N$ from left to right, each spaced 1 unit apart; similarly, there are $M$ horizontal roads numbered $1, 2, ..., M$ from bottom to top, each spaced 1 unit apart. We will denote the intersection between the $x$-th vertical road and the $y$-th horizontal road as $(x, y)$. 
Salmon has to make $K$ deliveries, with the $i$-th delivery starting at $(x_i, y_i)$ and ending at $(x'_i, y'_i)$. He can also travel every road with speed $0.5$ (meaning it would take him $2$ units of time to travel $1$ unit of distance). However, Salmon can bribe the mayor of Fish City and make the mayor change exactly one horizontal road to a highway, meaning the speed on that road would increase to $1$.
He wants to choose a road to be a highway such that the sum of durations of all the deliveries is minimum possible. Help him find this minimum sum!
Note that each delivery starts exactly at $(x_i, y_i)$ and ends at $(x'_i, y'_i)$, i.e., we don't count the time taken to travel from $(x'_{i-1}, y'_{i-1})$ to $(x_i, y_i)$ in our answer.

-----Input:-----
The first line contains 3 integers, $N$, $M$ and $K$ ($1 \le N, M, K \le 10^5$).
The next $K$ lines describe deliveries. Each line contains 4 space-separated integers $x_i$, $y_i$, $x'_i$, $y'_i$ ($1 \le x_i, x'_i \le N$, $1 \le y_i, y'_i \le M$), describing the $i$-th delivery.

-----Output:-----
Print one integer -- the minimum sum of durations possible.

-----Subtasks-----
- Subtask 1 [17 points]: $y_i = y_{i-1}$ for all $i>0$. 
- Subtask 2 [34 points]: $K \le 10$.
- Subtask 3 [49 points]: No additional constraints.

-----Sample Input 1:-----
5 4 3
2 3 4 1
1 4 5 2
3 3 5 3

-----Sample Output 1:-----
16

-----Explanation:-----

Salmon can turn the 3rd horizontal road into a highway.
- For the first delivery, we can go 2 units to the right taking 2 units of time, and 2 units down taking 4 units of time. The time taken is $2 + 4 = 6$.
- For the second delivery, we can go 1 unit down taking 2 units of time, 4 units right taking 4 units of time, and 1 unit down taking 2 units of time. The time taken is $2 + 4 + 2 = 8$.
- For the third delivery, we can go 2 units right taking 2 units of time.
Therefore, the total time taken is $6 + 8 + 2 = 16$.

-----Sample Input 2:-----
10 2 3
1 2 10 2
2 1 9 1
4 1 7 1

-----Sample Output 2:-----
23

-----Explanation:-----

Salmon can turn the 1st horizontal road into a highway.
- For the first delivery, we can go 1 unit down taking 2 units of time, 9 units right taking 9 units of time, and 1 unit up taking 2 units of time. The time taken is $2 + 9 + 2 = 13$.
- For the second delivery, we can go 7 units right taking 7 units of time.
- For the third delivery, we can go 3 units to the right taking 3 units of time.
Therefore, the total time taken is $13 + 7 + 3 = 23$.

```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\nimport statistics \nfrom statistics import mode\nreadline = sys.stdin.readline\ntry:\n  \n INF = 10**18+3\n N, M, K = map(int, readline().split())\n Points = [tuple(map(int, readline().split())) for _ in range(K)]\n ABC = [(p[1], p[3], abs(p[0] - p[2])) for p in Points]\n ans = INF\n l=[]\n if K <= 10:\n  ans = INF\n  for m in range(1, M+1):\n   res = 0\n   for a, b, c in ABC:\n    res += min(2*abs(a-m) + 2*abs(b-m) + c, 2*abs(a-b) + 2*c)\n   ans = min(ans, res)\n  print(ans)\n else:\n  def horiz():\n   ans=0\n \n   for yo,y1,x in ABC:\n     max1=0\n     lv=1\n     dist=[0]*M\n     if (yo-x//4)>1:\n      lv=yo-x//4\n     up=M\n     if (x//4+y1)<up:\n      up=x//4+y1\n     for j in range(lv,up+1):\n      if j < yo:\n       dist[j]+=x-4*(yo-j)\n      elif j>=yo and j<=y1:\n       dist[j]+=x\n      else:\n       dist[j]+=x-4*(j-y1)\n      if dist[j]>dist[max1]:\n       max1=j\n   return max1\n \n \n    \n  m = horiz()\n  res = 0\n  for a, b, c in ABC:\n   res += min(2*abs(a-m) + 2*abs(b-m) + c, 2*abs(a-b) + 2*c)\n  ans = min(ans, res)\n  print(ans)\nexcept:\n pass'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13573