Problem:
Score: 400 points

Problem Statement

Chokudai made a rectangular cake for contestants in DDCC 2020 Finals.

The cake has H - 1 horizontal notches and W - 1 vertical notches, which divide the cake into H \times W equal sections. K of these sections has a strawberry on top of each of them.

The positions of the strawberries are given to you as H \times W characters s_{i, j} (1 \leq i \leq H, 1 \leq j \leq W). If s_{i, j} is #, the section at the i-th row from the top and the j-th column from the left contains a strawberry; if s_{i, j} is ., the section does not contain one. There are exactly K occurrences of #s.

Takahashi wants to cut this cake into K pieces and serve them to the contestants. Each of these pieces must satisfy the following conditions:

Has a rectangular shape.

Contains exactly one strawberry.

One possible way to cut the cake is shown below:

Find one way to cut the cake and satisfy the condition. We can show that this is always possible, regardless of the number and positions of the strawberries.

Constraints

1 \leq H \leq 300

1 \leq W \leq 300

1 \leq K \leq H \times W

s_{i, j} is # or ..

There are exactly K occurrences of # in s.

Input

Input is given from Standard Input in the following format:

H W K
s_{1, 1} s_{1, 2} \cdots s_{1, W}
s_{2, 1} s_{2, 2} \cdots s_{2, W}
:
s_{H, 1} s_{H, 2} \cdots s_{H, W}

Output

Assign the numbers 1, 2, 3, \dots, K to the K pieces obtained after the cut, in any order. Then, let a_{i, j} be the number representing the piece containing the section at the i-th row from the top and the j-th column from the left of the cake. Output should be in the following format:

a_{1, 1} \ a_{1, 2} \ \cdots \ a_{1, W}
a_{2, 1} \ a_{2, 2} \ \cdots \ a_{2, W}
:
a_{H, 1} \ a_{H, 2} \ \cdots \ a_{H, W}

If multiple solutions exist, any of them will be accepted.

Sample Input 1

3 3 5
#.#
.#.
#.#

Sample Output 1

1 2 2
1 3 4
5 5 4

One way to cut this cake is shown below:

Sample Input 2

3 7 7
#...#.#
..#...#
.#..#..

Sample Output 2

1 1 2 2 3 4 4
6 6 2 2 3 5 5
6 6 7 7 7 7 7

One way to cut this cake is shown below:

Sample Input 3

13 21 106
.....................
.####.####.####.####.
..#.#..#.#.#....#....
..#.#..#.#.#....#....
..#.#..#.#.#....#....
.####.####.####.####.
.....................
.####.####.####.####.
....#.#..#....#.#..#.
.####.#..#.####.#..#.
.#....#..#.#....#..#.
.####.####.####.####.
.....................

Sample Output 3

12 12 23 34 45 45 60 71 82 93 93 2 13 24 35 35 17 28 39 50 50
12 12 23 34 45 45 60 71 82 93 93 2 13 24 35 35 17 28 39 50 50
12 12 56 89 89 89 60 104 82 31 31 46 13 24 35 35 61 61 39 50 50
12 12 67 67 100 100 60 9 9 42 42 57 13 24 6 72 72 72 72 72 72
12 12 78 5 5 5 20 20 20 53 68 68 90 24 6 83 83 83 83 83 83
16 16 27 38 49 49 64 75 86 97 79 79 90 101 6 94 94 105 10 21 21
16 16 27 38 49 49 64 75 86 97 79 79 90 101 6 94 94 105 10 21 21
32 32 43 54 65 65 80 11 106 95 22 22 33 44 55 55 70 1 96 85 85
32 32 43 54 76 76 91 11 106 84 84 4 99 66 66 66 81 1 96 74 74
14 14 3 98 87 87 102 11 73 73 73 4 99 88 77 77 92 92 63 63 63
25 25 3 98 87 87 7 29 62 62 62 15 99 88 77 77 103 19 30 52 52
36 36 47 58 69 69 18 29 40 51 51 26 37 48 59 59 8 19 30 41 41
36 36 47 58 69 69 18 29 40 51 51 26 37 48 59 59 8 19 30 41 41

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

using System;
using System.Collections.Generic;
using System.Linq;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            input_iter = LazyLoadAllLines();
            //------------------------------------------------//
            var h = Read<long>();
            var w = Read<long>();
            var k = Read<long>();
            //var s = Read();
            List<string> sls = new List<string>();
            for(int i = 0; i < h; ++i)
            {
                sls.Add(Read());
            }
            //var als = Read<long>(n);
            //var fls = Read<long>(n);
            //List<long> als = new List<long>(), bls = new List<long>();
            /*List<List<long>> abls = new List<List<long>>();
            List<long> cls = new List<long>();
            for (int i = 0; i < m; ++i)
            {
                abls.Add(Read<long>(2));
                --abls[i][0];
                --abls[i][1];
                cls.Add(Read<long>());
            }
            var q = Read<long>();
            List<List<long>> stls = new List<List<long>>();
            for (int i = 0; i < q; ++i)
            {
                stls.Add(Read<long>(2));
                --stls[i][0];
                --stls[i][1];
            }*/

            //als.Sort((l, r) => (int)(l - r));

            List<int[]> als = new List<int[]>();
            List<int> aTemp = new List<int>();
            int[] aTempSave = new int[] {0};
            var id = 1;
            var toCopyNum = 1;
            for(int i = 0; i < h; ++i)
            {
                if (sls[i].Contains('#'))
                {
                    // l -> r greed
                    var sharpId = -1;
                    for (int j = 0; j < w; ++j)
                    {
                        aTemp.Add(id);
                        if(sls[i][j] == '#')
                        {
                            sharpId = j;
                            ++id;
                        }
                    }
                    for (int j = sharpId + 1; j < w; ++j) --aTemp[j];

                    for (int j = 0; j < toCopyNum; ++j) als.Add(aTemp.ToArray());
                    toCopyNum = 1;
                    aTempSave = aTemp.ToArray();
                    aTemp.Clear();
                }
                else
                {
                    ++toCopyNum;
                }
            }

            if(toCopyNum > 1)
            {
                for (int j = 1; j < toCopyNum; ++j) als.Add(aTempSave);
            }

            for (int i = 0; i < h; ++i)
            {
                Console.WriteLine(string.Join(" ", als[i]));
            }
        }

        static IEnumerator<string> input_iter;

        static _T Read<_T>() where _T : struct
        {
            input_iter.MoveNext();
            return (_T)Convert.ChangeType(input_iter.Current, typeof(_T));
        }
        static string Read()
        {
            input_iter.MoveNext();
            return input_iter.Current;
        }
        static List<_T> Read<_T>(long num) where _T : struct { return new List<_T>(Enumerate<_T>(num)); }


        static IEnumerable<_T> Enumerate<_T>(long num)
        {
            for (long i = 0; i < num; ++i)
            {
                input_iter.MoveNext();
                yield return (_T)Convert.ChangeType(input_iter.Current, typeof(_T));
            }
        }
        static IEnumerator<string> LazyLoadAllLines()
        {
            string line;
            do
            {
                line = Console.ReadLine();
                foreach (var s in line.Split(' '))
                    yield return s;
            } while (line != null);
        }

        public class PriorityQueue<T> where T : IComparable
        {
            private IComparer<T> comparer = null;
            private bool isAccendingOrder;

            private List<T> heap;
            private int heapCurrentSize = 0;

            //public int Count { get; private set; } = 0;

            public PriorityQueue(IComparer<T> comparer, int initialHeapSize = 256)
            {
                heap = new List<T>(initialHeapSize);
                this.comparer = comparer;
            }

            public PriorityQueue(bool isAccending = true, int initialHeapSize = 256)
            {
                heap = new List<T>(initialHeapSize);
                isAccendingOrder = isAccending;
            }

            private int Compare(T x, T y)
            {
                if (comparer != null) return comparer.Compare(x, y);
                return isAccendingOrder ? x.CompareTo(y) : y.CompareTo(x);
            }

            public bool Empty()
            {
                return Count() == 0;
            }

            public int Count()
            {
                return heapCurrentSize;
            }

            public void Push(T x)
            {
                //node number
                var idx = heapCurrentSize++;
                if (heapCurrentSize > heap.Count) heap.Capacity *= 2;

                while (idx > 0)
                {
                    //parent node number
                    var parentIdx = (idx - 1) / 2;

                    if (Compare(heap[parentIdx], x) <= 0) break;

                    heap[idx] = heap[parentIdx];
                    idx = parentIdx;
                }

                heap[idx] = x;
            }

            public T Pop()
            {
                T ret = heap[0];
                T x = heap[--heapCurrentSize];

                int idx = 0;
                while (idx * 2 + 1 < heapCurrentSize)
                {
                    //children
                    int a = idx * 2 + 1;
                    int b = idx * 2 + 2;

                    if (b < heapCurrentSize && Compare(heap[b], heap[a]) < 0) a = b;

                    if (Compare(heap[a], x) >= 0) break;

                    heap[idx] = heap[a];
                    idx = a;
                }

                heap[idx] = x;

                return ret;
            }

            public T Peek()
            {
                return heap[0];
            }

            public bool Contains(T x)
            {
                for (int i = 0; i < heapCurrentSize; i++) if (x.Equals(heap[i])) return true;
                return false;
            }

            public void Clear()
            {
                while (heapCurrentSize > 0) Pop();
            }

            public IEnumerator<T> GetEnumerator()
            {
                var temp = new List<T>();

                while (heapCurrentSize > 0)
                {
                    temp.Add(Pop());
                }

                foreach (var value in temp)
                {
                    Push(value);
                    yield return value;
                }
            }

            public T[] ToArray()
            {
                T[] array = new T[heapCurrentSize];
                int i = 0;

                foreach (var r in this)
                {
                    array[i] = r;
                    ++i;
                }

                return array;
            }
        }
    }
}