Problem: problem

There is a light bulb at the grid point $ (x, y) $ that meets $ 1 \ leq x \ leq h, 1 \ leq y \ leq w $.

The power supply is installed at coordinates $ (i + 0.5, j + 0.5) (1 \ leq i <h, 1 \ leq j <w, i + j $ is even) (corrected at 14:21). Coordinates $ When the power supply installed at (i + 0.5, j + 0.5) $ is turned on, the coordinates $ (i, j), (i + 1, j), (i, j + 1), (i + 1) , j + 1) $ 4 $ light bulbs in $ glow.

If you have more than $ 1 $ connected to a power supply with a light bulb on $ (i, j) $, you get $ B_ {i, j} $ cleanliness. You have the total cleanliness. Also, if you turn on each power supply, it costs $ W $ for electricity per $ 1 $.

Turn on some power to maximize "total income-total electricity bill".



output

Output the maximum value of "total income-total electricity bill". Also, output a line break at the end.

Example

Input

4 4 10
100 100 100 100
100 100 100 100
1 100 100 1
1 1 1 1


Output

970

Solution (in CPP):

Solution:
// need
#include <iostream>
#include <algorithm>
// data structure
#include <bitset>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#include <complex>
//#include <deque>
#include <valarray>
#include <unordered_map>
#include <unordered_set>
#include <array>
// stream
//#include <istream>
#include <sstream>
//#include <ostream>
#include <fstream>
// etc
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
#include <chrono>
#include <random>
#include <numeric>

// input
#define INIT std::ios::sync_with_stdio(false);std::cin.tie(0);
#define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__);
template<typename T> void MACRO_VAR_Scan(T& t) { std::cin >> t; }
template<typename First, typename...Rest>void MACRO_VAR_Scan(First& first, Rest&...rest) { std::cin >> first; MACRO_VAR_Scan(rest...); }
#define VEC_ROW(type, n, ...)std::vector<type> __VA_ARGS__;MACRO_VEC_ROW_Init(n, __VA_ARGS__); for(int w_=0; w_<n; ++w_){MACRO_VEC_ROW_Scan(w_, __VA_ARGS__);}
template<typename T> void MACRO_VEC_ROW_Init(int n, T& t) { t.resize(n); }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Init(int n, First& first, Rest&...rest) { first.resize(n); MACRO_VEC_ROW_Init(n, rest...); }
template<typename T> void MACRO_VEC_ROW_Scan(int p, T& t) { std::cin >> t[p]; }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Scan(int p, First& first, Rest&...rest) { std::cin >> first[p]; MACRO_VEC_ROW_Scan(p, rest...); }
#define VEC(type, c, n) std::vector<type> c(n);for(auto& i:c)std::cin>>i;
#define MAT(type, c, m, n) std::vector<std::vector<type>> c(m, std::vector<type>(n));for(auto& R:c)for(auto& w:R)std::cin>>w;
// output
#define OUT(dist) std::cout<<(dist);
#define FOUT(n, dist) std::cout<<std::fixed<<std::setprecision(n)<<(dist);
#define SOUT(n, c, dist) std::cout<<std::setw(n)<<std::setfill(c)<<(dist);
#define SP std::cout<<" ";
#define TAB std::cout<<"\t";
#define BR std::cout<<"\n";
#define SPBR(w, n) std::cout<<(w + 1 == n ? '\n' : ' ');
#define ENDL std::cout<<std::endl;
#define FLUSH std::cout<<std::flush;
#define SHOW(dist) {std::cerr << #dist << "\t:" << (dist) << "\n";}
#define SHOWVECTOR(v) {std::cerr << #v << "\t:";for(const auto& xxx : v){std::cerr << xxx << " ";}std::cerr << "\n";}
#define SHOWVECTOR2(v) {std::cerr << #v << "\t:\n";for(const auto& xxx : v){for(const auto& yyy : xxx){std::cerr << yyy << " ";}std::cerr << "\n";}}
#define SHOWQUEUE(a) {auto tmp(a);std::cerr << #a << "\t:";while(!tmp.empty()){std::cerr << tmp.front() << " ";tmp.pop();}std::cerr << "\n";}
// utility
#define ALL(a) (a).begin(),(a).end()
#define FOR(w, a, n) for(int w=(a);w<(n);++w)
#define RFOR(w, a, n) for(int w=(n)-1;w>=(a);--w)
#define REP(w, n) for(int w=0;w<int(n);++w)
#define RREP(w, n) for(int w=int(n)-1;w>=0;--w)
#define FORLL(w, a, n) for(ll w=ll(a);w<ll(n);++w)
#define RFORLL(w, a, n) for(ll w=ll(n)-1;w>=ll(a);--w)
#define REPLL(w, n) for(ll w=0;w<ll(n);++w)
#define RREPLL(w, n) for(ll w=ll(n)-1;w>=0;--w)
#define IN(a, x, b) (a<=x && x<b)
template<class T> inline T CHMAX(T& a, const T b) { return a = (a < b) ? b : a; }
template<class T> inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; }
#define EXCEPTION(msg) throw std::string("Exception : " msg " [ in ") + __func__ + " : " + std::to_string(__LINE__) + " lines ]"
#define TRY(cond, msg) try {if (cond) EXCEPTION(msg);}catch (std::string s) {std::cerr << s << std::endl;}

// test
template<class T> using V = std::vector<T>;
template<class T> using VV = V<V<T>>;

template<typename S, typename T>
std::ostream& operator<<(std::ostream& os, std::pair<S, T> p) {
	os << "(" << p.first << ", " << p.second << ")"; return os;
}

#define random_shuffle "USE std::shuffle!";

// type/const
#define int ll
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PAIR = std::pair<int, int>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = 1 << 30;                          // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;              // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                          // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62);  // 9.22x10^18
constexpr double EPS = 1e-6;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;
template<class T, size_t N> void FILL(T(&a)[N], const T& val) { for (auto& x : a) x = val; }
template<class ARY, size_t N, size_t M, class T> void FILL(ARY(&a)[N][M], const T& val) { for (auto& b : a) FILL(b, val); }
template<class T> void FILL(std::vector<T>& a, const T& val) { for (auto& x : a) x = val; }
template<class ARY, class T> void FILL(std::vector<std::vector<ARY>>& a, const T& val) { for (auto& b : a) FILL(b, val); }
// ------------>8------------------------------------->8------------

// Dinic法
class Dinic {
private:
	struct Edge {
		int to, cap, rev;
		Edge(int t, int c, int r) :to(t), cap(c), rev(r) {}
	};
	int V;
	std::vector<std::vector<Edge>> graph;
	std::vector<int> level, iter;

public:
	Dinic(int v) : V(v) {
		graph.resize(v);
		level.resize(v, -1);
		iter.resize(v, 0);
	}
	// fromからtoへ向かう容量capの辺をグラフに追加する
	void addEdge(int from, int to, int cap) {
		graph[from].emplace_back(to, cap, graph[to].size());
		graph[to].emplace_back(from, 0, graph[from].size() - 1);
	}

	// sからの最短距離をBFSで計算する
	void bfs(int s) {
		std::fill(level.begin(), level.end(), -1);
		std::queue<int> queue;
		level[s] = 0;
		queue.push(s);
		while (!queue.empty()) {
			int v = queue.front(); queue.pop();
			for (int i = 0; i < graph[v].size(); ++i) {
				Edge& e = graph[v][i];
				if (e.cap > 0 && level[e.to] < 0) {
					level[e.to] = level[v] + 1;
					queue.push(e.to);
				}
			}
		}
	}

	// 増加パスをDFSで探す
	int dfs(int v, int t, int f) {
		if (v == t) return f;
		for (int& i = iter[v]; i < graph[v].size(); ++i) {
			Edge& e = graph[v][i];
			if (e.cap > 0 && level[v] < level[e.to]) {
				int d = dfs(e.to, t, std::min(f, e.cap));
				if (d > 0) {
					e.cap -= d;
					graph[e.to][e.rev].cap += d;
					return d;
				}
			}
		}
		return 0;
	}

	// sからtへの最大流を求める
	int maxFlow(int s, int t) {
		int res = 0;
		while (true) {
			bfs(s);
			if (level[t] < 0) return res;
			std::fill(iter.begin(), iter.end(), 0);
			int f;
			while ((f = dfs(s, t, INFLL)) > 0) {
				res += f;
			}
		}
	}
};

signed main() {
	INIT;

	VAR(int, h, w, W);
	MAT(int, b, h, w);

	int sum = 0;
	REP(i, h) REP(j, w) sum += b[i][j];

	V<PAIR> lamp;
	REP(i, h - 1) REP(j, w - 1) {
		if ((i + j) % 2 == 0) lamp.emplace_back(i, j);
	}

	const int N = h * w;
	const int S = N + lamp.size(), T = S + 1;
	Dinic dn(N + lamp.size() + 2);

	auto convert = [&](int y, int x) {
		return y * w + x;
	};

	int dy4[] = { 0, 0, 1, 1 };
	int dx4[] = { 0, 1, 0, 1 };

	REP(i, lamp.size()) {
		auto& p = lamp[i];
		if (p.first % 2 == 0) {
			dn.addEdge(S, N + i, W);
			dn.addEdge(N + i, T, 0);
			REP(d, 4) {
				dn.addEdge(N + i, convert(p.first + dy4[d], p.second + dx4[d]), b[p.first + dy4[d]][p.second + dx4[d]]);
			}
		}
		else {
			dn.addEdge(S, N + i, 0);
			dn.addEdge(N + i, T, W);
			REP(d, 4) {
				dn.addEdge(convert(p.first + dy4[d], p.second + dx4[d]), N + i, b[p.first + dy4[d]][p.second + dx4[d]]);
			}
		}
	}
	REP(i, h) {
		dn.addEdge(convert(i, 0 + 0), T, INFLL);
		dn.addEdge(convert(i, w - 1), T, INFLL);
	}
	REP(j, w) {
		dn.addEdge(convert(0 + 0, j), T, INFLL);
		dn.addEdge(convert(h - 1, j), T, INFLL);
	}

	int mf = dn.maxFlow(S, T);

	OUT(sum - mf)BR;

	return 0;
}