Problem:
Score : 600 points

Problem Statement

There is a board with N rows and M columns.
The information of this board is represented by N strings S_1,S_2,\ldots,S_N.
Specifically, the state of the square at the i-th row from the top and the j-th column from the left is represented as follows:

S_{i,j}=. : the square is empty.

S_{i,j}=# : an obstacle is placed on the square.

S_{i,j}=o : a piece is placed on the square.

Yosupo repeats the following operation:

Choose a piece and move it to its right adjecent square or its down adjacent square.
Moving a piece to squares with another piece or an obstacle is prohibited.
Moving a piece out of the board is also prohibited.

Yosupo wants to perform the operation as many times as possible.
Find the maximum possible number of operations.

Constraints

1 \leq N \leq 50

1 \leq M \leq 50

S_i is a string of length M consisting of ., # and o.

1 \leq ( the number of pieces )\leq 100.
In other words, the number of pairs (i, j) that satisfy S_{i,j}=o is between 1 and 100, both inclusive.

Input

Input is given from Standard Input in the following format:

N M
S_1
S_2
\vdots
S_N

Output

Print the maximum possible number of operations in a line.

Sample Input 1

3 3
o..
...
o.#

Sample Output 1

4

Yosupo can perform operations 4 times as follows:

o.. .o. ..o ... ...
... -> ... -> ... -> ..o -> ..o
o.# o.# o.# o.# .o#

Sample Input 2

9 10
.#....o#..
.#..#..##o
.....#o.##
.###.#o..o
#.#...##.#
..#..#.###
#o.....#..
....###..o
o.......o#

Sample Output 2

24

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#line 2 "/Users/kaage/Desktop/ProgrammingWorkspace/library/other/template.hpp"
#define _CRT_SECURE_NO_WARNINGS
#pragma target("avx2")
#pragma optimize("O3")
#pragma optimize("unroll-loops")
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <string.h>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define rep(i,n) for(int i=0;i<(n);i++)
#define REP(i,n) for(int i=1;i<=(n);i++)
#define all(V) V.begin(),V.end()
typedef unsigned int uint;
typedef long long lint;
typedef unsigned long long ulint;
typedef std::pair<int, int> P;
typedef std::pair<lint, lint> LP;
constexpr int INF = INT_MAX/2;
constexpr lint LINF = LLONG_MAX/2;
constexpr double eps = DBL_EPSILON;
constexpr double PI=3.141592653589793238462643383279;
template<class T>
class prique :public std::priority_queue<T, std::vector<T>, std::greater<T>> {};
template <class T, class U>
inline bool chmax(T& lhs, const U& rhs) {
	if (lhs < rhs) {
		lhs = rhs;
		return 1;
	}
	return 0;
}
template <class T, class U>
inline bool chmin(T& lhs, const U& rhs) {
	if (lhs > rhs) {
		lhs = rhs;
		return 1;
	}
	return 0;
}
inline lint gcd(lint a, lint b) {
	while (b) {
		lint c = a;
		a = b; b = c % b;
	}
	return a;
}
inline lint lcm(lint a, lint b) {
	return a / gcd(a, b) * b;
}
bool isprime(lint n) {
	if (n == 1)return false;
	for (int i = 2; i * i <= n; i++) {
		if (n % i == 0)return false;
	}
	return true;
}
template<typename T>
T mypow(T a, lint b) {
	T res(1);
	while(b){
		if(b&1)res*=a;
		a*=a;
		b>>=1;
	}
	return res;
}
lint modpow(lint a, lint b, lint m) {
	lint res(1);
	while(b){
		if(b&1){
			res*=a;res%=m;
		}
		a*=a;a%=m;
		b>>=1;
	}
	return res;
}
template<typename T>
void printArray(std::vector<T>& vec) {
	rep(i, vec.size()){
		std::cout << vec[i];
		std::cout<<(i==(int)vec.size()-1?"\n":" ");
	}
}
template<typename T>
void printArray(T l, T r) {
	T rprev = std::prev(r);
	for (T i = l; i != rprev; i++) {
		std::cout << *i << " ";
	}
	std::cout << *rprev << std::endl;
}
LP extGcd(lint a,lint b) {
	if(b==0)return {1,0};
	LP s=extGcd(b,a%b);
	std::swap(s.first,s.second);
	s.second-=a/b*s.first;
	return s;
}
LP ChineseRem(const lint& b1,const lint& m1,const lint& b2,const lint& m2) {
	lint p=extGcd(m1,m2).first;
	lint tmp=(b2-b1)*p%m2;
	lint r=(b1+m1*tmp+m1*m2)%(m1*m2);
	return std::make_pair(r,m1*m2);
}
template<typename F>
inline constexpr decltype(auto) lambda_fix(F&& f){
	return [f=std::forward<F>(f)](auto&&... args){
		return f(f,std::forward<decltype(args)>(args)...);
	};
}
#line 3 "/Users/kaage/Desktop/ProgrammingWorkspace/library/graph/MinCostFlow.hpp"
class MinCostFlow{
    class edge{
    public:
        int to,cap;
        lint cost;
        int rev,id;
    };
    int n,idx=0,s,t;
    lint curres=0;
    std::vector<std::vector<edge>> vec;
    std::vector<int> prevv,preve;
    std::vector<lint> h,dist;
    bool negative=false;
    lint BellmanFord(){
        dist.assign(n,LINF);
        dist[s]=0;
        rep(i,n-1){
            rep(j,n){
                rep(k,vec[j].size()){
                    const edge &e=vec[j][k];
                    if(e.cap>0&&chmin(dist[e.to],dist[j]+e.cost+h[j]-h[e.to])){
                        prevv[e.to]=j;
                        preve[e.to]=k;
                    }
                }
            }
        }
        if(dist[t]==LINF){
            std::cerr<<"The demand is over maximum flow."<<std::endl;
            return -1;
        }
        rep(i,n)h[i]+=dist[i];
        for(int i=t;i!=s;i=prevv[i]){
            vec[prevv[i]][preve[i]].cap--;
            vec[i][vec[prevv[i]][preve[i]].rev].cap++;
        }
        return h[t];
    }
public:
    MinCostFlow(int n,int s,int t):n(n),s(s),t(t){
        vec.resize(n);
        h.resize(n);
        dist.resize(n);
        prevv.resize(n);
        preve.resize(n);
    }
    void add_edge(int from,int to,int cap,lint cost){
        if(cost<0)negative=true;
        vec[from].push_back({to,cap,cost,(int)vec[to].size(),-1});
        vec[to].push_back({from,0,-cost,(int)vec[from].size()-1,idx++});
    }
    lint add_flow(int f){
        if(negative){
            curres+=BellmanFord();
            f--;
            negative=false;
        }
        while(f>0){
            dist.assign(n,LINF);
            dist[s]=0;
            prique<LP> que;
            que.push({0,s});
            while(!que.empty()){
                LP p=que.top();
                que.pop();
                if(dist[p.second]<p.first)continue;
                rep(i,vec[p.second].size()){
                    edge &e=vec[p.second][i];
                    if(e.cap>0&&chmin(dist[e.to],dist[p.second]+e.cost+h[p.second]-h[e.to])){
                        prevv[e.to]=p.second;
                        preve[e.to]=i;
                        que.push({dist[e.to],e.to});
                    }
                }
            }
            if(dist[t]==LINF){
                std::cerr<<"The demand is over the maximum flow."<<std::endl;
                return -1;
            }
            rep(i,n)h[i]+=dist[i];
            int d=f;
            for(int i=t;i!=s;i=prevv[i]){
                chmin(d,vec[prevv[i]][preve[i]].cap);
            }
            f-=d;
            curres+=(lint)d*h[t];
            for(int i=t;i!=s;i=prevv[i]){
                vec[prevv[i]][preve[i]].cap-=d;
                vec[i][vec[prevv[i]][preve[i]].rev].cap+=d;
            }
        }
        return curres;
    }
    std::vector<lint> restore(){
        std::vector<lint> res(idx);
        rep(i,n){
            for(const auto& j:vec[i]){
                if(j.id!=-1)res[j.id]=j.cap;
            }
        }
        return res;
    }
    void reset(){
        rep(i,n){
            for(auto& j:vec[i]){
                if(j.id!=-1){
                    vec[j.to][j.rev].cap+=j.cap;
                    j.cap=0;
                }
            }
        }
    }
};
#line 3 "main.cpp"
int N,M;
char S[51][51];
int main(){
	std::cin>>N>>M;
	MinCostFlow mcf(N*M+2,0,N*M+1);
	int cnt=0;
	rep(i,N){
		rep(j,M){
			std::cin>>S[i][j];
			if(S[i][j]=='o'){
				mcf.add_edge(0,i*M+j+1,1,0);
				cnt++;
			}
			if(S[i][j]!='#')mcf.add_edge(i*M+j+1,N*M+1,1,0);
		}
	}
	rep(i,N){
		rep(j,M){
			if(S[i][j]=='#')continue;
			if(i!=N-1&&S[i+1][j]!='#')mcf.add_edge(i*M+j+1,(i+1)*M+j+1,3000,-1);
			if(j!=M-1&&S[i][j+1]!='#')mcf.add_edge(i*M+j+1,i*M+j+2,3000,-1);
		}
	}
	std::cout<<-mcf.add_flow(cnt)<<std::endl;
	return 0;
}