Problem:
Score : 400 points

Problem Statement

There is a grid with H horizontal rows and W vertical columns, and there are obstacles on some of the squares.

Snuke is going to choose one of the squares not occupied by an obstacle and place a lamp on it.
The lamp placed on the square will emit straight beams of light in four cardinal directions: up, down, left, and right.
In each direction, the beam will continue traveling until it hits a square occupied by an obstacle or it hits the border of the grid. It will light all the squares on the way, including the square on which the lamp is placed, but not the square occupied by an obstacle.

Snuke wants to maximize the number of squares lighted by the lamp.

You are given H strings S_i (1 \leq i \leq H), each of length W. If the j-th character (1 \leq j \leq W) of S_i is #, there is an obstacle on the square at the i-th row from the top and the j-th column from the left; if that character is ., there is no obstacle on that square.

Find the maximum possible number of squares lighted by the lamp.

Constraints

1 \leq H \leq 2,000

1 \leq W \leq 2,000

S_i is a string of length W consisting of # and ..

. occurs at least once in one of the strings S_i (1 \leq i \leq H).

Input

Input is given from Standard Input in the following format:

H W
S_1
:
S_H

Output

Print the maximum possible number of squares lighted by the lamp.

Sample Input 1

4 6
#..#..
.....#
....#.
#.#...

Sample Output 1

8

If Snuke places the lamp on the square at the second row from the top and the second column from the left, it will light the following squares: the first through fifth squares from the left in the second row, and the first through fourth squares from the top in the second column, for a total of eight squares.

Sample Input 2

8 8
..#...#.
....#...
##......
..###..#
...#..#.
##....#.
#...#...
###.#..#

Sample Output 2

13

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using static System.Math;
using static AtCoderTemplate.MyConstants;
using static AtCoderTemplate.MyInputOutputs;
using static AtCoderTemplate.MyNumericFunctions;
using static AtCoderTemplate.MyAlgorithm;
using static AtCoderTemplate.MyExtensions;

namespace AtCoderTemplate {
    public class Program {
        public static void Main (string[] args) {
            var HW = ReadInts ();
            var H = HW[0];
            var W = HW[1];
            var S = Enumerable.Range (0, H).Select (i => Read ().Select (c => c.ToString ()).ToList ()).ToList ();
            var L = new int[H, W];
            foreach (var i in MyEnumerable.Interval (0, H)) {
                foreach (var j in MyEnumerable.Interval (0, W)) {
                    if (S[i][j] == "#") {
                        L[i, j] = 0;
                    } else if (j == 0) {
                        L[i, j] = 1;
                    } else {
                        L[i, j] = L[i, j - 1] + 1;
                    }
                }
            }
            var R = new int[H, W];
            foreach (var i in MyEnumerable.Interval (0, H)) {
                foreach (var j in MyEnumerable.Interval (0, W).Reverse ()) {
                    if (S[i][j] == "#") {
                        R[i, j] = 0;
                    } else if (j == W - 1) {
                        R[i, j] = 1;
                    } else {
                        R[i, j] = R[i, j + 1] + 1;
                    }
                }
            }
            var U = new int[H, W];
            foreach (var i in MyEnumerable.Interval (0, H)) {
                foreach (var j in MyEnumerable.Interval (0, W)) {
                    if (S[i][j] == "#") {
                        U[i, j] = 0;
                    } else if (i == 0) {
                        U[i, j] = 1;
                    } else {
                        U[i, j] = U[i - 1, j] + 1;
                    }
                }
            }
            var D = new int[H, W];
            foreach (var i in MyEnumerable.Interval (0, H).Reverse ()) {
                foreach (var j in MyEnumerable.Interval (0, W)) {
                    if (S[i][j] == "#") {
                        D[i, j] = 0;
                    } else if (i == H - 1) {
                        D[i, j] = 1;
                    } else {
                        D[i, j] = D[i + 1, j] + 1;
                    }
                }
            }

            var max = MyEnumerable.Interval (0, H).Select (i =>
                MyEnumerable.Interval (0, W).Select (j =>
                    L[i, j] + R[i, j] + U[i, j] + D[i, j] - 3
                ).Max ()
            ).Max ();
            Print (max);
        }
    }

    public static class MyInputOutputs {
        /* Input & Output*/
        public static string Read () {
            return Console.ReadLine ();
        }

        public static List<string> Reads () {
            return Console.ReadLine ().Split (' ').ToList ();
        }

        public static List<List<string>> ReadRows (int rowNum) {
            /*
            入力例
            A1 B1 C1 ... Z1
            A2 B2 C2 ... Z2
            ...
            An Bn Cn ... Zn
           

            出力例
            [[A1, B1, C1, ... Z1], [A2, B2, C2, ... Z2], ... [An, Bn, Cn, ... Zn]]
            */
            return Enumerable.Range (0, rowNum).Select (i => Reads ()).ToList ();
        }

        public static List<List<string>> ReadColumns (int rowNum, int colNum) {
            /*
            入力例
            A1 B1 C1 ... Z1
            A2 B2 C2 ... Z2
            ...
            An Bn Cn ... Zn
           

            出力例
            [[A1, A2, A3, ... An], [B1, B2, B3, ... Bn], ... [Z1, Z2, Z3, ... Zn]]
            */
            var rows = ReadRows (rowNum);
            return Enumerable.Range (0, colNum).Select (i => rows.Select (items => items[i].ToString ()).ToList ()).ToList ();
        }

        public static int ToInt (this string str) {
            return int.Parse (str);
        }

        public static long ToLong (this string str) {
            return long.Parse (str);
        }

        public static List<int> ToInts (this List<string> strs) {
            return strs.Select (str => str.ToInt ()).ToList ();
        }

        public static List<long> ToLongs (this List<string> strs) {
            return strs.Select (str => str.ToLong ()).ToList ();
        }

        public static int ReadInt () {
            return Read ().ToInt ();
        }
        public static long ReadLong () {
            return Read ().ToLong ();
        }

        public static List<int> ReadInts () {
            return Reads ().ToInts ();
        }
        public static List<long> ReadLongs () {
            return Reads ().ToLongs ();
        }

        public static void Print<T> (T item) {
            Console.WriteLine (item);
        }
        public static void PrintIf<T1, T2> (bool condition, T1 trueResult, T2 falseResult) {
            if (condition) {
                Console.WriteLine (trueResult);
            } else {
                Console.WriteLine (falseResult);
            }
        }

        public static void PrintRow<T> (IEnumerable<T> list) {
            /* 横ベクトルで表示
            A B C D ...
            */
            if (!list.IsEmpty ()) {
                Console.Write (list.First ());
                foreach (var item in list.Skip (1)) {
                    Console.Write ($" {item}");
                }
            }
            Console.Write ("\n");
        }
        public static void PrintColomn<T> (IEnumerable<T> list) {
            /* 縦ベクトルで表示
            A
            B
            C
            D
            ...
            */
            foreach (var item in list) {
                Console.WriteLine (item);
            }
        }
        public static void PrintRows<T> (IEnumerable<IEnumerable<T>> sources) {
            foreach (var row in sources) {
                PrintRow (row);
            }
        }
    }

    public static class MyConstants {
        public static IEnumerable<char> lowerAlphabets = Enumerable.Range ('a', 'z' - 'a' + 1).Select (i => (char) i);
        public static IEnumerable<char> upperAlphabets = Enumerable.Range ('A', 'Z' - 'A' + 1).Select (i => (char) i);

        public static int p10_9plus7 = (int) Pow (10, 9) + 7;
    }

    public static class MyNumericFunctions {
        public static bool IsEven (int a) {
            return a % 2 == 0;
        }
        public static bool IsEven (long a) {
            return a % 2 == 0;
        }
        public static bool IsOdd (int a) {
            return !IsEven (a);
        }
        public static bool IsOdd (long a) {
            return !IsEven (a);
        }

        /// <summary>
        /// 冪を得る
        /// </summary>
        /// <param name="b">底</param>
        /// <param name="n">冪指数</param>
        /// <param name="divisor">返り値がintを超えないようにdivisorで割ったあまりを得る</param>
        /// <returns>bのn乗(をdivisorで割ったあまり)</returns>
        public static int PowRem (long b, int n, int divisor) {
            return Enumerable.Repeat (b, n)
                .Aggregate (1, (accm, i) => (int) ((accm * i) % divisor));
        }

        /// <summary>
        /// 順列の総数を得る
        /// O(N-K)
        /// </summary>
        /// <param name="n">全体の数</param>
        /// <param name="k">並べる数</param>
        /// <param name="divisor">返り値がintを超えないようにdivisorで割った余りを得る</param>
        /// <returns>nPk (をdivisorで割った余り)</returns>
        public static int nPk (int n, int k, int divisor) {
            if (k > n) {
                return 0;
            } else {
                return Enumerable.Range (n - k + 1, k).Aggregate (1, ((i, m) => (i * m) % divisor));
            }
        }

        public static long nPk (int n, int k) {
            if (k > n) {
                return 0L;
            } else {
                return Enumerable.Range (n - k + 1, k).Aggregate (1L, ((i, m) => (i * m)));
            }
        }

        /// <summary>
        /// 階乗を得る
        /// O(N)
        /// </summary>
        /// <param name="n"></param>
        /// <param name="divisor">返り値がintを超えないようにdivisorで割った余りを得る</param>
        /// <returns>n! (をdivisorで割った余り)</returns>
        public static int Fact (int n, int divisor) {
            return nPk (n, n, divisor);
        }

        public static long Fact (int n) {
            return nPk (n, n);
        }

        /// <summary>
        /// 組み合わせの総数を得る
        /// </summary>
        /// <param name="n"></param>
        /// <param name="k"></param>
        /// <returns>nCk</returns>
        public static long nCk (int n, int k) {
            if (k > n) {
                return 0L;
            } else {
                return nPk (n, k) / Fact (k);
            }
        }

        /// <summary>
        /// 最大公約数を得る 
        /// O(log N)
        /// </summary>
        /// <param name="m">自然数</param>
        /// <param name="n">自然数</param>
        /// <returns></returns>
        public static long GCD (long m, long n) {
            // GCD(m,n) = GCD(n, m%n)を利用
            // m%n = 0のとき、mはnで割り切れるので、nが最大公約数
            if (m <= 0L || n <= 0L) throw new ArgumentOutOfRangeException ();

            if (m < n) return GCD (n, m);
            while (m % n != 0L) {
                var n2 = m % n;
                m = n;
                n = n2;
            }
            return n;
        }

        /// <summary>
        /// 最小公倍数を得る
        /// O(log N)
        /// </summary>
        /// <param name="m"></param>
        /// <param name="n"></param>
        /// <returns></returns>
        public static long LCM (long m, long n) {
            var ans = checked ((long) (BigInteger.Multiply (m, n) / GCD (m, n)));
            return ans;
        }

        /// <summary>
        /// 約数列挙(非順序)
        /// O(√N)
        /// </summary>
        /// <param name="m">m > 0</param>
        /// <returns></returns>
        public static IEnumerable<long> Divisor (long m) {
            if (!(m > 0)) throw new ArgumentOutOfRangeException ();

            var front = Enumerable.Range (1, (int) Sqrt (m))
                .Select (i => (long) i)
                .Where (d => m % d == 0);
            return front.Concat (front.Where (x => x * x != m).Select (x => m / x));
        }

        public static IEnumerable<int> Divisor (int m) {
            if (!(m > 0)) throw new ArgumentOutOfRangeException ();

            var front = Enumerable.Range (1, (int) Sqrt (m))
                .Where (d => m % d == 0);
            return front.Concat (front.Where (x => x * x != m).Select (x => m / x));
        }

        /// <summary>
        /// 公約数列挙(非順序)
        /// O(√N)
        /// </summary>
        /// <param name="m">m > 0</param>
        /// <param name="n">n > 0 </param>
        /// <returns></returns>
        public static IEnumerable<long> CommonDivisor (long m, long n) {
            if (!(m > 0)) throw new ArgumentOutOfRangeException ();

            if (m < n) return CommonDivisor (n, m);
            return Divisor (m).Where (md => n % md == 0);
        }

        public static IEnumerable<int> CommonDivisor (int m, int n) {
            if (!(m > 0)) throw new ArgumentOutOfRangeException ();

            if (m < n) return CommonDivisor (n, m);
            return Divisor (m).Where (md => n % md == 0);
        }

        /// <summary>
        /// nまでの素数を得る
        /// </summary>
        /// <param name="n">n > 1</param>
        /// <returns></returns>
        public static IEnumerable<int> Prime (int n) {
            if (!(n > 1)) throw new ArgumentOutOfRangeException ();

            var primes = new List<int> ();
            foreach (var i in Enumerable.Range (2, n - 1)) {
                if (primes.All (p => i % p != 0)) {
                    primes.Add (i);
                }
            }
            return primes;
        }

        /// <summary>
        /// 順列を得る
        /// O(N!)
        /// </summary>
        public static IEnumerable<IEnumerable<T>> Perm<T> (IEnumerable<T> source, int n) {
            if (n == 0 || source.IsEmpty () || source.Count () < n) {
                return Enumerable.Empty<IEnumerable<T>> ();
            } else if (n == 1) {
                return source.Select (i => new List<T> { i });
            } else {
                var nexts = source.Select ((x, i) =>
                    new { next = source.Take (i).Concat (source.Skip (i + 1)), selected = source.Take (i + 1).Last () });
                return nexts.SelectMany (next => Perm (next.next, n - 1).Select (item => item.Prepend (next.selected)));
            }
        }
    }

    public static class MyAlgorithm {
        /// <summary>
        /// めぐる式二分探索法
        /// O(log N)
        /// </summary>
        /// <param name="list">探索するリスト</param>
        /// <param name="predicate">条件の述語関数</param>
        /// <param name="ng">条件を満たさない既知のindex</param>
        /// <param name="ok">条件を満たす既知のindex</param>
        /// <returns>条件を満たすindexの内、隣がfalseとなるtrueのindexを返す</returns>
        public static int BinarySearch<T> (List<T> list, Func<T, bool> predicate, int ng, int ok) {
            while (Abs (ok - ng) > 1) {
                int mid = (ok + ng) / 2;
                if (predicate (list[mid])) {
                    ok = mid;
                } else {
                    ng = mid;
                }
            }
            return ok;
        }

        /// <summary>
        /// 左二分探索法
        /// </summary>
        /// <param name="list">条件の境界(falseとtrueの変わるところ)で、trueが左にあるリスト</param>
        /// <param name="predicate">条件の述語関数</param>
        /// <returns>左隣がfalseになるtrueのindexを返す</returns>
        public static int LeftBinarySearch<T> (List<T> list, Func<T, bool> predicate) {
            return BinarySearch (list, predicate, list.Count, -1);
        }

        /// <summary>
        /// 右二分探索法
        /// </summary>
        /// <param name="list">条件の境界(falseとtrueの変わるところ)で、trueが右にあるリスト</param>
        /// <param name="predicate">条件の述語関数</param>
        /// <returns>左隣がfalseになるtrueのindexを返す</returns>
        public static int RightBinarySearch<T> (List<T> list, Func<T, bool> predicate) {
            return BinarySearch (list, predicate, -1, list.Count);
        }

        // Dictionaryがcapacity近くになるとゲロ重かったので削除
        // 配列にするかも

        // /// <summary>
        // /// DynamicProgrammingの形式(貰うDP)
        // /// 項dp_(i,j,k...)の漸化式、初項、漸化式の計算順序（添字のパターン）、から漸化式を計算する
        // /// </summary>
        // /// <param name="calculationOrders">漸化式の計算順序、項dp_(i,j,k...)の添字(i,j,k...)のトポロジカル順序を持つシーケンス</param>
        // /// <param name="initialConditions">初項とその添字のペア、のシーケンス</param>
        // /// <param name="recurrenceRelation">項dp_(i,j,k...)の漸化式、以前の項の計算はDictonaryから得る</param>
        // /// <typeparam name="Indexes">項dp_(i,j,k...)の添字(i,j,k...)</typeparam>
        // /// <typeparam name="Result">項dp_(i,j,k...)の計算結果</typeparam>
        // /// <returns>項dp_(i,j,k...)の全ての計算結果をDictionaryで返す</returns>
        // public static Dictionary<Indexes, Result> DynamicProgramming<Indexes, Result> (
        //     IEnumerable<Indexes> calculationOrders //
        //     , IEnumerable<KeyValuePair<Indexes, Result>> initialConditions //
        //     , Func<Dictionary<Indexes, Result>, Indexes, Result> recurrenceRelation) {
        //     var conditions = initialConditions.ToDictionary (kv => kv.Key, kv => kv.Value);
        //     foreach (var order in calculationOrders) {
        //         conditions.Add (order, recurrenceRelation (conditions, order));
        //     }
        //     return conditions;
        // }

        // .NetFramework 4.6.2 ではタプルの記法がまだ使えない

        // /// <summary>
        // /// DynamicProgrammingの形式(貰うDP)
        // /// 項dp_(i,j,k...)の漸化式、初項、漸化式の計算順序（添字のパターン）、から漸化式を計算する
        // /// </summary>
        // /// <param name="calculationOrders">漸化式の計算順序、項dp_(i,j,k...)の添字(i,j,k...)のトポロジカル順序を持つシーケンス</param>
        // /// <param name="initialConditions">初項とその添字のペア、のシーケンス</param>
        // /// <param name="recurrenceRelation">項dp_(i,j,k...)の漸化式、以前の項の計算はDictonaryから得る</param>
        // /// <typeparam name="Indexes">項dp_(i,j,k...)の添字(i,j,k...)</typeparam>
        // /// <typeparam name="Result">項dp_(i,j,k...)の計算結果</typeparam>
        // /// <returns>項dp_(i,j,k...)の全ての計算結果をDictionaryで返す</returns>
        // public static Dictionary<Indexes, Result> DynamicProgramming<Indexes, Result> (
        //     IEnumerable<Indexes> calculationOrders //
        //     , IEnumerable < (Indexes indexes, Result result) > initialConditions //
        //     , Func<Dictionary<Indexes, Result>, Indexes, Result> recurrenceRelation) {
        //     var conditions = initialConditions.ToDictionary (kv => kv.indexes, kv => kv.result);
        //     foreach (var order in calculationOrders) {
        //         conditions.Add (order, recurrenceRelation (conditions, order));
        //     }
        //     return conditions;
        // }

        /// <summary>
        /// 右へのしゃくとり法の形式
        /// </summary>
        /// <param name="n">なめるシーケンスの長さ</param>
        /// <param name="Predicate">更新のための条件関数。indexの(left,right)をとり、条件を満たすとUpdateConditionを行う</param>
        /// <param name="initialCondition">初期状態。</param>
        /// <param name="Update">状態更新関数。indexのleft, rightと前のconditionをとり、更新したconditionを返す</param>
        /// <typeparam name="TR"></typeparam>
        /// <returns></returns>
        public static TR TwoPointersRight<TR> (int n, Func<int, int, bool> Predicate, TR initialCondition, Func<int, int, TR, TR> Update) {
            var l = 0;
            var r = 0;
            TR condition = initialCondition;
            while (r < n) {
                while (r < n && !Predicate (l, r)) {
                    r += 1;
                }
                while (r < n && l != r && Predicate (l, r)) {
                    condition = Update (l, r, condition);
                    l += 1;
                }
            }
            return condition;
        }

        /// <summary>
        /// 重み付きの辺
        /// </summary>
        public struct WeightEdge {
            int SourceNode { get; }
            int TargetNode { get; }
            long Weight { get; }

            public WeightEdge (int sourceNode, int targetNode, long weight) {
                SourceNode = sourceNode;
                TargetNode = targetNode;
                Weight = weight;
            }
        }

        public static List<WeightEdge> ToWeightEdges (List<int> sourceNodes, List<int> targetNodes, List<long> weights) {
            return Enumerable.Range (0, sourceNodes.Count)
                .Select (i => new WeightEdge (sourceNode: sourceNodes[i], targetNode: targetNodes[i], weight: weights[i]))
                .ToList ();
        }

        /// <summary>
        /// 重み付きグラフ
        /// </summary>
        public class WeightGraph {
            long[, ] adjacencyMatrix;
            public int NodeNum { get; }
            public WeightGraph (int nodeNum, long weightOfNoEdge) {
                var adjacencyMatrix = new long[nodeNum, nodeNum];
                foreach (var i in Enumerable.Range (0, nodeNum)) {
                    foreach (var j in Enumerable.Range (0, nodeNum)) {
                        if (i != j) {
                            adjacencyMatrix[i, j] = weightOfNoEdge;
                        } else {
                            adjacencyMatrix[i, j] = 0;
                        }
                    }
                }

                this.adjacencyMatrix = adjacencyMatrix;
                this.NodeNum = nodeNum;
            }

            public WeightGraph (List<WeightEdge> edges, int nodeNum, long weightOfNoEdge) {
                var adjacencyMatrix = new long[nodeNum, nodeNum];
                foreach (var edge in edges) {

                }
            }

            public WeightGraph (WeightGraph graph) {
                this.adjacencyMatrix = new long[graph.NodeNum, graph.NodeNum];
                foreach (var i in Enumerable.Range (0, graph.NodeNum)) {
                    foreach (var j in Enumerable.Range (0, graph.NodeNum)) {
                        this.adjacencyMatrix[i, j] = graph.GetLength (i, j);
                    }
                }
                this.NodeNum = graph.NodeNum;
            }

            public List<List<long>> ToList () {
                return Enumerable.Range (0, NodeNum).Select (i =>
                    Enumerable.Range (0, NodeNum).Select (j =>
                        adjacencyMatrix[i, j]
                    ).ToList ()
                ).ToList ();
            }

            public void Add (int node1, int node2, long distance) {
                adjacencyMatrix[node1, node2] = distance;
            }

            public long GetLength (int node1, int node2) {
                return adjacencyMatrix[node1, node2];
            }
        }

        /// <summary>
        /// ワーシャルフロイド法
        /// O(N^3)
        /// </summary>
        /// <param name="graph">グラフ</param>
        /// <param name="nodeNum">ノードの数</param>
        /// <returns>各ノード間の最短距離を辺として持つグラフ</returns>
        public static WeightGraph WarshallFloyd (WeightGraph graph) {
            var res = new WeightGraph (graph);
            foreach (var b in Enumerable.Range (0, graph.NodeNum)) {
                foreach (var a in Enumerable.Range (0, graph.NodeNum)) {
                    foreach (var c in Enumerable.Range (0, graph.NodeNum)) {
                        res.Add (a, c, Min (res.GetLength (a, c), res.GetLength (a, b) + res.GetLength (b, c)));
                    }
                }
            }
            return res;
        }
    }

    public static class MyExtensions {
        // AppendとPrependが、.NET Standard 1.6からの追加で、Mono 4.6.2 はそれに対応して仕様はあるが、実装がない
        public static IEnumerable<T> Append<T> (this IEnumerable<T> source, T element) {
            return source.Concat (Enumerable.Repeat (element, 1));
        }

        public static IEnumerable<T> Prepend<T> (this IEnumerable<T> source, T element) {
            return Enumerable.Repeat (element, 1).Concat (source);
        }

        // TakeLastとSkipLastが、.Net Standard 2.1からの追加で、Mono 4.6.2 はそれに対応していない
        public static IEnumerable<T> TakeLast<T> (this IEnumerable<T> source, int count) {
            return source.Skip (source.Count () - count);
        }

        public static IEnumerable<T> SkipLast<T> (this IEnumerable<T> source, int count) {
            return source.Take (source.Count () - count);
        }

        public static bool IsEmpty<T> (this IEnumerable<T> source) {
            return !source.Any ();
        }

        public static IEnumerable<T> Do<T> (this IEnumerable<T> source, Action<T> action) {
            foreach (var item in source) {
                action (item);
            }
            return source;
        }

        public static TR Pipe<T, TR> (this T arg, Func<T, TR> func) {
            return func (arg);
        }

        /// <summary>
        /// シーケンスの隣り合う要素を2引数の関数に適用したシーケンスを得る
        /// </summary>
        /// <para>O(N)</para>
        /// <param name="source">元のシーケンス</param>
        /// <param name="func">2引数関数</param>
        /// <example>[1,2,3,4].MapAdjacent(f) => [f(1,2), f(2,3), f(3,4)]</example>
        public static IEnumerable<TR> MapAdjacent<T1, TR> (this IEnumerable<T1> source, Func<T1, T1, TR> func) {
            var list = source.ToList ();
            return Enumerable.Range (1, list.Count - 1)
                .Select (i => func (list[i - 1], list[i]));
        }

        /// <summary>
        /// 累積項を要素にもつシーケンスを得る(初項は、first)
        /// <para>O(N)</para>
        /// </summary>
        /// <param name="source">元のシーケンス</param>
        /// <param name="func">2引数関数f</param>
        /// <param name="first">func(first, source[0])のための初項</param>
        /// <example> [1,2,3].Scanl1(0,f) => [0, f(0,1), f(f(0,1),2), f(f(f(0,1),2),3)]</example>
        public static IEnumerable<TR> Scanl<T, TR> (this IEnumerable<T> source, TR first, Func<TR, T, TR> func) {
            var list = source.ToList ();
            var result = new List<TR> { first };
            foreach (var i in Enumerable.Range (0, source.Count ())) {
                result.Add (func (result[i], list[i]));
            }
            return result;
        }
        /// <summary>
        /// 累積項を要素にもつシーケンスを得る（初項は、source.First()）
        /// <para>O(N)</para>
        /// </summary>
        /// <param name="source">要素数1以上のシーケンス</param>
        /// <param name="func">2引数関数f</param>
        /// <example> [1,2,3].Scanl1(f) => [1, f(1,2), f(f(1,2),3)]</example>
        public static IEnumerable<T> Scanl1<T> (this IEnumerable<T> source, Func<T, T, T> func) {
            if (source.IsEmpty ()) throw new ArgumentOutOfRangeException ();
            var list = source.ToList ();
            var result = new List<T> { list[0] };
            foreach (var i in Enumerable.Range (1, source.Count () - 1)) {
                result.Add (func (result[i - 1], list[i]));
            }
            return result;
        }
    }

    public static class MyEnumerable {

        /// <summary>
        /// 左閉右開区間 [startIndex,endIndex) を得る
        /// </summary>
        /// <param name="startIndex">始まりのインデックス。含む</param>
        /// <param name="endIndex">終わりのインデックス。含まない</param>
        public static IEnumerable<int> Interval (int startIndex, int endIndex) {
            if (endIndex - startIndex < 0) new ArgumentException ();
            return Enumerable.Range (startIndex, endIndex - startIndex);
        }
    }
}