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

public class Skyscrapers {
    private static IEnumerable<List<T>> Permutations<T>(List<T> initial)
        where T: IComparable<T> {
        yield return initial;

        var hasNext = initial.Count > 1;
        while (hasNext) {
            var k = 0;
            var l = 0;
            hasNext = false;

            for (var i = initial.Count - 1; i > 0; i--) {
                if (initial[i].CompareTo(initial[i - 1]) > 0) {
                    k = i - 1;
                    hasNext = true;
                    break;
                }
            }

            for (var i = initial.Count - 1; i > k; i--) {
                if (initial[i].CompareTo(initial[k]) > 0) {
                    l = i;
                    break;
                }
            }

            (initial[k], initial[l]) = (initial[l], initial[k]);
            initial.Reverse(k + 1, initial.Count - k - 1);

            if (hasNext) {
                yield return initial;
            }
        }
    }

    private static bool IsValid(List<int> heights, int clue) {
        var canSee = 1;
        var lastHeight = heights[0];

        for (var i = 1; i < heights.Count; i++) {
            var currentHeight = heights[i];
            if (currentHeight > lastHeight) {
                lastHeight = currentHeight;
                canSee++;
            }
        }

        return canSee == clue;
    }

    private static IEnumerable<List<int>> PossibleHeights(int size, int clue) {
        var initial = new List<int>();
        for (var i = 0; i < size; i++) {
            initial.Add(i + 1);
        }

        if (clue == 0) {
          return Permutations(initial);
        }

        return Permutations(initial).Where(heights => IsValid(heights, clue));
    }

    private static int Size {
        get => 4;
    }

    private static (int, int) GetDiffs(int clueIndex) {
        if (clueIndex < Size) {
            return (0, 1);
        } else if (clueIndex < 2 * Size) {
            return (-1, 0);
        } else if (clueIndex < 3 * Size) {
            return (0, -1);
        }
        return (1, 0);
    }

    private static (int, int) GetStarts(int clueIndex) {
        if (clueIndex < Size) {
            return (clueIndex, 0);
        } else if (clueIndex < 2 * Size) {
            return (Size - 1, clueIndex % Size);
        } else if (clueIndex < 3 * Size) {
            return (Size - 1 - clueIndex % Size, Size - 1);
        }
        return (0, Size - 1 - clueIndex % Size);
    }

    private static List<int> BackupHeights(int[][] heights, int clueIndex) {
        var backup = new List<int>();

        var (dx, dy) = GetDiffs(clueIndex);
        for (
            var (x, y) = GetStarts(clueIndex);
            x >= 0 && x < Size && y >= 0 && y < Size;
            x += dx, y += dy
        ) {
            backup.Add(heights[y][x]);
        }

        return backup;
    }

    private static bool EmplaceHeights(
        int[][] heights, int clueIndex, List<int> newHeights, bool force
    ) {
        int i = 0;

        var (dx, dy) = GetDiffs(clueIndex);
        for (
            var (x, y) = GetStarts(clueIndex);
            x >= 0 && x < Size && y >= 0 && y < Size;
            x += dx, y += dy
        ) {
            if (
                !force && heights[y][x] != 0 && heights[y][x] != newHeights[i]
            ) {
                return false;
            }

            heights[y][x] = newHeights[i++];
        }

        return true;
    }

    private static bool SolvePuzzle(
        int[][] heights, int[] clues, int clueIndex, bool ignoreZeroes
    ) {
        while (clueIndex < 4 * Size && (
            (ignoreZeroes && clues[clueIndex] == 0) || (!ignoreZeroes && clues[clueIndex] != 0)
        )) {
            clueIndex++;
        }

        if (clueIndex >= 4 * Size) {
            return true;
        }

        // create copy of heights to ensure correct resetting
        var currentHeights = BackupHeights(heights, clueIndex);

        // iterate through the options
        foreach (var possibleHeights in PossibleHeights(Size, clues[clueIndex])) {
            // emplace heights and if conflict occurs, reset and try next one
            if (!EmplaceHeights(heights, clueIndex, possibleHeights, false)) {
                EmplaceHeights(heights, clueIndex, currentHeights, true);
                continue;
            }

            // if no conflict present, try filling out other clues
            if (SolvePuzzle(heights, clues, clueIndex + 1, ignoreZeroes)) {
                return true;
            }

            // otherwise reset heights and try again
            EmplaceHeights(heights, clueIndex, currentHeights, true);
        }

        // if we got here, there is no feasible configuration of buildings
        return false;
    }

    public static int[][] SolvePuzzle(int[] clues) {
        var result = new int[Size][];
        for (var i = 0; i < Size; i++) {
            result[i] = new int[Size];
        }
        SolvePuzzle(result, clues, 0, true);

        // in case there are left zeroes
        SolvePuzzle(result, clues, 0, false);

        return result;
    }
}