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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Globalization;
using System.IO;
using System.Text;
using System.Linq;

using E = System.Linq.Enumerable;
using System.Threading;
using Weight = System.Int64;

internal partial class Solver {
    public void Run() {
        var n = ni();
        var m = ni();
        var s = ns(n);

        int toId(int row, int col) => row * m + col;
        int source = n * m;
        int sink = source + 1;

        var pd = new PrimalDual(sink + 1);
        var infCapacity = 1000000000;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (s[i][j] == 'o') pd.AddEdge(source, toId(i, j), 1, 0);
                if (i + 1 < n && s[i][j] != '#' && s[i + 1][j] != '#') pd.AddEdge(toId(i, j), toId(i + 1, j), infCapacity, -1);
                if (j + 1 < m && s[i][j] != '#' && s[i][j + 1] != '#') pd.AddEdge(toId(i, j), toId(i, j + 1), infCapacity, -1);
                if (s[i][j] != '#') pd.AddEdge(toId(i, j), sink, 1, 0);
            }
        }

        cout.WriteLine(-pd.Run(source, sink, 100000).TotalCost);
    }

}


public class MinCostFlowResult {
    public Weight TotalCost;
    public Weight TotalFlow;
}
public class PrimalDual {
    private readonly int N;
    private readonly List<List<Edge>> adjacents;

    private readonly Weight[] _distance;
    private readonly bool[] _inQueue;
    private readonly Edge[] _prevEdges;
    private readonly Queue<int> _queue;

    public class Edge {
        public int From, To;
        public Weight Flow, Capacity, Cost;
        public Edge Reverse;
        public Edge(int from, int to, Weight capacity, Weight cost, Weight flow = 0) {
            From = from;
            To = to;
            Cost = cost;
            Flow = flow;
            Capacity = capacity;
        }
        public Weight Residue {
            get {
                return Capacity - Flow;
            }
        }
    }

    public PrimalDual(int n) {
        N = n;
        adjacents = new List<List<Edge>>();
        for (int i = 0; i < n; i++) {
            adjacents.Add(new List<Edge>());
        }
        _distance = new Weight[N];
        _inQueue = new bool[N];
        _prevEdges = new Edge[N];
        _queue = new Queue<int>(N);
    }

    public IEnumerable<Edge> GetEdges() {
        return adjacents.SelectMany(a => a);
    }

    public void AddEdge(int from, int to, Weight capacity, Weight cost) {
        var e = new Edge(from, to, capacity, cost);
        adjacents[from].Add(e);
    }

    private Edge[] FindShortestPathTree(int source) {
        Array.Clear(_inQueue, 0, _inQueue.Length);
        Array.Clear(_prevEdges, 0, _prevEdges.Length);
        for (int i = 0; i < N; i++) {
            _distance[i] = Weight.MaxValue;
        }
        _distance[source] = 0;
        _inQueue[source] = true;
        _queue.Enqueue(source);
        while (_queue.Count > 0) { // SPFA
            int now = _queue.Dequeue();
            _inQueue[now] = false;
            foreach (var e in adjacents[now]) {
                if (e.Residue <= 0) {
                    continue;
                }

                if (_distance[now] != Weight.MaxValue && _distance[e.To] > _distance[now] + e.Cost) {
                    _distance[e.To] = _distance[now] + e.Cost;
                    _prevEdges[e.To] = e;
                    if (!_inQueue[e.To]) {
                        _inQueue[e.To] = true;
                        _queue.Enqueue(e.To);
                    }
                }
            }
        }
        return _prevEdges;
    }

    public MinCostFlowResult Run(int source, int sink, Weight flow) {
        Weight totalCost = 0;
        Weight totalFlow = 0;

        while (totalFlow < flow) {
            var prevEdges = FindShortestPathTree(source);
            if (prevEdges[sink] == null) {
                break;
            }

            long incrementalFlow = flow - totalFlow;
            for (var e = prevEdges[sink]; e != null; e = prevEdges[e.From]) {
                incrementalFlow = Math.Min(incrementalFlow, e.Residue);
            }
            for (var e = prevEdges[sink]; e != null; e = prevEdges[e.From]) {
                if (e.Reverse == null) {
                    var reverseEdge = new Edge(e.To, e.From, 0, -e.Cost) {
                        Reverse = e
                    };
                    e.Reverse = reverseEdge;
                    adjacents[e.To].Add(reverseEdge);
                }
                totalCost += e.Cost * incrementalFlow;
                e.Flow += incrementalFlow;
                e.Reverse.Flow -= incrementalFlow;
            }
            totalFlow += incrementalFlow;
        }
        return new MinCostFlowResult { TotalCost = totalCost, TotalFlow = totalFlow };
    }
}
// PREWRITEN CODE BEGINS FROM HERE

static public class StringExtensions {
    static public string JoinToString<T>(this IEnumerable<T> source, string separator = " ") {
        return string.Join(separator, source);
    }
}

internal partial class Solver : Scanner {
    static readonly int? StackSizeInMebiByte = null; //50;
    public static void StartAndJoin(Action action, int maxStackSize) {
        var thread = new Thread(new ThreadStart(action), maxStackSize);
        thread.Start();
        thread.Join();
    }

    public static void Main() {
#if LOCAL
        byte[] inputBuffer = new byte[1000000];
        var inputStream = Console.OpenStandardInput(inputBuffer.Length);
        using (var reader = new StreamReader(inputStream, Console.InputEncoding, false, inputBuffer.Length)) {
            Console.SetIn(reader);
            new Solver(Console.In, Console.Out).Run();
        }
#else
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        if (StackSizeInMebiByte.HasValue) {
            StartAndJoin(() => new Solver(Console.In, Console.Out).Run(), StackSizeInMebiByte.Value * 1024 * 1024);
        } else {
            new Solver(Console.In, Console.Out).Run();
        }
        Console.Out.Flush();
#endif
    }

#pragma warning disable IDE0052
    private readonly TextReader cin;
    private readonly TextWriter cout;
    private readonly TextWriter cerr;
#pragma warning restore IDE0052

    public Solver(TextReader reader, TextWriter writer)
        : base(reader) {
        cin = reader;
        cout = writer;
        cerr = Console.Error;
    }

    public Solver(string input, TextWriter writer)
        : this(new StringReader(input), writer) {
    }

#pragma warning disable IDE1006
#pragma warning disable IDE0051
    private int ni() { return NextInt(); }
    private int[] ni(int n) { return NextIntArray(n); }
    private long nl() { return NextLong(); }
    private long[] nl(int n) { return NextLongArray(n); }
    private double nd() { return NextDouble(); }
    private double[] nd(int n) { return NextDoubleArray(n); }
    private string ns() { return Next(); }
    private string[] ns(int n) { return NextArray(n); }
#pragma warning restore IDE1006
#pragma warning restore IDE0051
}

#if DEBUG
internal static class LinqPadExtension {
    public static string TextDump<T>(this T obj) {
        if (obj is IEnumerable) return (obj as IEnumerable).Cast<object>().JoinToString().Dump();
        else return obj.ToString().Dump();
    }
    public static T Dump<T>(this T obj) {
        return LINQPad.Extensions.Dump(obj);
    }
}
#endif

public class Scanner {
    private readonly TextReader Reader;
    private readonly CultureInfo ci = CultureInfo.InvariantCulture;

    private readonly char[] buffer = new char[2 * 1024];
    private int cursor = 0, length = 0;
    private string Token;
    private readonly StringBuilder sb = new StringBuilder(1024);

    public Scanner()
        : this(Console.In) {
    }

    public Scanner(TextReader reader) {
        Reader = reader;
    }

    public int NextInt() { return checked((int)NextLong()); }
    public long NextLong() {
        var s = Next();
        long r = 0;
        int i = 0;
        bool negative = false;
        if (s[i] == '-') {
            negative = true;
            i++;
        }
        for (; i < s.Length; i++) {
            r = r * 10 + (s[i] - '0');
#if DEBUG
            if (!char.IsDigit(s[i])) throw new FormatException();
#endif
        }
        return negative ? -r : r;
    }
    public double NextDouble() { return double.Parse(Next(), ci); }
    public string[] NextArray(int size) {
        string[] array = new string[size];
        for (int i = 0; i < size; i++) {
            array[i] = Next();
        }

        return array;
    }
    public int[] NextIntArray(int size) {
        int[] array = new int[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextInt();
        }

        return array;
    }

    public long[] NextLongArray(int size) {
        long[] array = new long[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextLong();
        }

        return array;
    }

    public double[] NextDoubleArray(int size) {
        double[] array = new double[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextDouble();
        }

        return array;
    }

    public string Next() {
        if (Token == null) {
            if (!StockToken()) {
                throw new Exception();
            }
        }
        var token = Token;
        Token = null;
        return token;
    }

    public bool HasNext() {
        if (Token != null) {
            return true;
        }

        return StockToken();
    }

    private bool StockToken() {
        while (true) {
            sb.Clear();
            while (true) {
                if (cursor >= length) {
                    cursor = 0;
                    if ((length = Reader.Read(buffer, 0, buffer.Length)) <= 0) {
                        break;
                    }
                }
                var c = buffer[cursor++];
                if (33 <= c && c <= 126) {
                    sb.Append(c);
                } else {
                    if (sb.Length > 0) break;
                }
            }

            if (sb.Length > 0) {
                Token = sb.ToString();
                return true;
            }

            return false;
        }
    }
}