const Pathfinder = struct {
    const Grid = @import("grid.zig").Grid;
    const Graph = @import("graph.zig").Graph;
};

const std = @import("std");
const Grid = @import("grid.zig").Grid;
test "Grid" {
    var t = try std.time.Timer.start();
    var d = try Grid(usize, 100, 100).ParseGridFromCSV("grid-test.txt", ",");
    const ret = try d.dijkstra(std.testing.allocator, .{ 0, 0 }, .{ 99, 99 });
    std.debug.print("time: {d}us\n", .{t.read() / 1_000});
    try std.testing.expectEqual(@as(usize, 366), ret);
}

const std = @import("std");
const Str = []const u8;
pub fn Grid(comptime T: type, comptime GRID_ROWS: usize, comptime GRID_COLS: usize) type {
    return struct {
        grid: [GRID_ROWS][GRID_COLS]T,
        pub fn ParseGridFromCSV(comptime path: Str, sep: Str) !@This() {
            const input = @embedFile(path);
            var lines = std.mem.tokenize(u8, input, "\n");
            var ret: [GRID_ROWS][GRID_COLS]T = undefined;
            var row: usize = 0;
            while (lines.next()) |line| : (row += 1) {
                var items = std.mem.tokenize(u8, line, sep);
                var col: usize = 0;
                while (items.next()) |item| : (col += 1) {
                    // TODO: use proper parse function for each type
                    ret[row][col] = try std.fmt.parseUnsigned(T, item, 0);
                }
            }
            return @This(){
                .grid = ret,
            };
        }
        const QueueType = struct {
            state: [2]usize,
            cost: usize,
        };
        fn lessThan(context: void, a: QueueType, b: QueueType) std.math.Order {
            _ = context;
            if (a.cost == b.cost) {
                return .eq;
            } else if (a.cost < b.cost) {
                return .lt;
            } else {
                return .gt;
            }
        }
        pub fn dijkstra(self: @This(), allocator: std.mem.Allocator, start: [2]usize, end: [2]usize) !usize {
            var CostGrid = [_][GRID_COLS]usize{[_]usize{~@as(usize, 0)} ** GRID_COLS} ** GRID_ROWS;
            CostGrid[start[0]][start[1]] = 0;
            var queue = std.PriorityQueue(QueueType, void, comptime lessThan).init(allocator, {});
            defer queue.deinit();
            try queue.add(.{ .state = start, .cost = 0 });
            // XXX: add AutoNeighbours()!
            const directions = [_][2]i2{
                .{ -1, 0 },
                .{ 1, 0 },
                .{ 0, -1 },
                .{ 0, 1 },
            };
            while (queue.count() > 0) {
                const curr = queue.remove();
                if (std.meta.eql(curr.state, end)) {
                    return curr.cost;
                }
                for (directions) |d| {
                    const diffrow = @intCast(isize, curr.state[0]) + d[0];
                    if (diffrow < 0 or diffrow >= GRID_ROWS) continue;
                    const dr = @intCast(usize, diffrow);
                    const diffcol = @intCast(isize, curr.state[1]) + d[1];
                    if (diffcol < 0 or diffcol >= GRID_COLS) continue;
                    const dc = @intCast(usize, diffcol);
                    const cost = CostGrid[curr.state[0]][curr.state[1]] +| self.grid[dr][dc];
                    if (cost < CostGrid[dr][dc]) {
                        CostGrid[dr][dc] = cost;
                        try queue.add(.{ .state = .{ dr, dc }, .cost = cost });
                    }
                }
            }
            unreachable;
        }
    };
}

1,9,6,8,4,6,4,9,1,6,1,1,2,1,9,1,3,9,1,6,1,1,2,8,1,1,5,1,9,1,9,8,4,5,3,6,1,2,9,9,1,5,3,4,1,5,8,9,1,1,9,8,1,5,4,2,6,8,9,5,9,1,3,2,6,4,1,1,1,4,6,9,4,8,1,7,6,1,2,2,6,7,2,1,8,8,3,8,4,6,2,5,8,3,4,9,1,8,7,9
1,5,2,5,7,1,1,2,1,6,1,3,3,1,4,2,1,9,5,6,1,9,4,1,5,7,3,6,5,1,1,8,4,4,8,1,1,1,9,6,7,1,2,7,8,2,5,5,6,1,1,1,3,7,8,1,7,2,2,2,2,2,1,2,1,1,2,8,4,6,9,3,2,2,7,2,4,1,1,8,9,6,1,1,9,1,5,5,8,1,6,6,2,4,8,1,9,2,1,2
2,1,4,3,6,3,1,1,6,2,3,6,1,9,1,2,2,2,1,9,2,2,2,3,7,3,6,1,3,9,1,3,9,3,3,3,9,3,2,8,2,3,1,9,1,2,1,1,8,3,1,3,1,7,9,3,6,3,1,8,7,1,9,7,5,1,1,9,7,1,8,8,7,9,6,1,7,7,1,6,1,7,3,3,1,7,3,2,1,9,4,2,3,9,5,8,6,2,2,7
2,5,2,1,6,2,5,3,1,4,1,2,1,4,4,1,8,9,9,4,1,3,9,4,8,9,5,1,2,2,4,9,3,5,6,5,4,6,1,1,2,6,1,1,6,8,6,4,4,2,5,2,1,7,3,4,3,3,1,1,1,3,7,9,1,1,8,1,4,4,9,1,8,5,9,1,2,6,1,3,5,2,8,4,5,1,3,3,9,3,1,1,1,1,3,6,3,2,1,1
3,4,1,9,1,1,6,3,9,5,1,7,1,3,1,6,7,5,4,2,6,3,1,4,4,6,1,9,3,1,6,1,2,1,1,1,9,1,4,1,7,8,9,7,9,1,1,5,6,1,7,6,1,3,3,4,9,1,1,1,9,1,7,2,4,1,3,8,3,5,7,3,1,8,1,2,1,4,3,1,2,8,3,3,9,4,6,2,1,5,7,2,1,1,7,1,4,8,3,2
4,5,2,4,9,6,4,1,5,3,2,4,7,4,2,8,3,1,9,3,1,4,1,2,9,9,1,2,9,1,1,2,9,9,5,3,7,3,2,1,1,4,9,1,3,3,3,7,6,5,2,3,1,3,1,7,1,2,3,9,5,2,3,9,2,9,7,6,1,1,3,8,5,5,5,1,5,2,1,2,3,2,1,8,7,2,4,8,8,6,6,7,3,2,2,6,2,3,1,4
3,7,1,1,5,6,9,9,2,2,5,7,2,1,1,2,3,1,1,1,1,1,2,3,1,3,8,1,6,2,1,5,6,9,8,1,9,6,1,3,1,1,5,8,2,4,1,5,2,6,2,3,2,1,1,1,4,9,1,5,3,8,9,2,1,1,4,3,5,1,9,3,8,5,2,6,4,8,3,5,1,3,9,9,4,1,3,1,8,9,9,2,2,1,2,4,6,1,8,4
9,3,7,2,2,1,8,2,1,1,2,2,7,9,2,3,2,9,1,1,1,6,5,1,4,1,6,3,6,4,7,1,3,1,2,8,1,5,4,2,6,5,1,4,5,8,9,2,8,5,4,4,3,1,9,2,7,2,1,1,5,3,3,3,8,2,9,6,5,3,2,1,2,2,8,3,2,1,8,2,1,3,5,7,2,3,4,6,1,5,1,2,7,1,1,4,8,3,1,4
7,2,5,2,4,3,9,6,1,2,4,3,6,9,2,8,7,2,1,1,9,7,3,2,4,1,4,2,7,6,1,1,6,5,1,3,3,3,4,5,6,1,4,5,1,8,7,2,5,4,2,7,6,4,3,2,2,7,2,1,1,2,9,1,2,6,1,8,4,8,3,1,1,8,2,2,3,6,4,9,1,1,6,6,9,2,1,9,4,4,7,1,2,3,9,2,2,1,3,4
3,1,2,4,2,2,2,2,8,5,3,3,8,3,2,7,5,1,4,9,1,1,6,2,2,1,2,1,5,5,7,6,3,9,1,9,2,2,3,1,7,7,5,7,2,1,6,1,9,2,4,1,4,5,5,8,1,1,9,1,2,4,1,9,7,1,4,1,8,6,2,9,6,1,1,1,7,5,4,8,9,2,1,4,4,1,1,6,2,6,9,5,1,8,3,1,6,1,7,4
5,1,1,3,4,3,1,5,1,2,4,1,6,8,1,1,1,8,6,1,6,2,1,1,9,5,8,6,1,8,4,2,1,9,5,1,3,1,5,4,1,1,5,6,5,4,7,3,2,5,1,2,8,3,4,8,3,2,9,4,4,6,2,2,3,3,1,2,7,2,2,1,2,6,7,3,4,2,2,2,1,1,4,1,3,2,1,5,4,7,3,1,6,8,5,4,1,1,1,4
8,9,1,8,7,6,1,2,6,3,1,1,5,1,1,1,4,3,2,5,7,3,1,3,1,4,1,7,3,4,4,9,1,4,4,5,6,8,1,5,1,2,1,3,1,2,1,5,1,1,4,3,6,2,6,7,5,1,5,7,2,9,9,7,9,6,4,9,3,1,3,6,7,1,4,4,9,3,1,1,1,1,3,2,2,2,2,1,9,1,9,4,3,1,1,8,4,5,3,9
2,3,1,5,1,1,2,8,6,8,2,1,1,2,1,5,1,1,9,1,2,3,3,9,1,4,3,6,2,1,4,8,5,1,8,9,2,1,3,2,4,3,8,1,1,7,1,9,8,4,1,1,3,6,1,7,3,2,9,3,5,2,1,3,3,8,9,2,1,9,3,2,1,9,1,3,1,1,1,2,8,6,3,5,6,9,9,1,5,8,1,6,1,7,1,1,2,3,1,1
8,2,1,3,4,3,9,2,7,8,4,2,6,5,1,8,9,1,6,8,4,1,3,2,1,1,5,8,9,1,5,3,3,8,8,7,1,7,5,1,1,5,7,5,1,1,5,1,1,5,1,2,4,1,1,5,2,6,3,6,2,5,7,2,1,8,6,5,8,1,3,5,3,2,5,2,4,9,3,2,5,1,1,6,1,6,4,2,3,2,1,3,3,1,3,1,9,2,3,8
3,8,1,4,6,4,8,2,1,2,3,1,2,2,1,7,7,3,2,2,2,4,2,1,5,3,6,5,1,1,6,4,2,2,2,9,2,4,1,3,3,1,5,9,3,1,2,5,1,1,8,2,6,6,7,6,9,1,2,1,2,1,4,1,2,5,1,1,9,2,2,6,1,1,2,9,3,1,4,1,3,3,6,1,1,3,4,1,1,1,1,1,2,1,1,8,3,6,2,5
1,6,3,2,1,5,3,2,8,2,1,1,5,8,2,7,1,9,9,4,9,4,2,1,9,4,7,8,5,1,6,8,4,8,8,1,9,4,2,9,4,3,9,4,2,1,1,4,6,1,6,2,4,6,4,3,8,1,5,7,2,1,1,6,2,7,1,2,5,1,1,2,7,1,9,1,3,2,3,1,1,1,9,2,1,2,2,1,7,8,1,8,2,1,5,6,1,2,2,9
2,9,6,4,9,9,3,9,8,2,2,7,5,4,1,1,1,2,3,5,1,1,3,2,1,1,1,4,1,9,4,4,2,2,1,1,3,8,1,5,9,2,2,4,4,9,4,5,8,3,1,2,2,6,1,1,9,5,9,3,9,4,2,4,1,1,5,8,9,9,9,9,1,8,4,6,1,3,9,3,1,8,4,3,3,1,4,1,6,2,3,1,7,5,6,9,9,4,2,2
3,1,8,5,9,1,1,1,3,2,2,2,2,2,2,5,8,8,2,1,2,8,9,1,1,4,2,5,2,3,1,7,1,1,1,9,3,1,2,1,1,6,2,1,1,4,9,9,3,2,4,5,1,5,8,8,1,3,3,9,6,4,3,3,4,9,3,1,3,2,1,4,2,1,5,6,1,1,2,3,5,3,2,1,2,1,9,1,8,8,1,3,1,1,2,2,2,2,4,3
2,5,9,7,4,1,9,1,7,6,1,1,7,8,7,2,6,2,3,3,7,2,2,5,7,5,4,7,9,6,3,2,8,8,1,1,4,3,5,9,1,9,8,2,7,4,1,2,3,1,1,1,2,1,7,1,1,1,5,1,5,1,1,7,1,3,4,5,8,2,4,7,1,2,1,3,8,3,5,3,7,9,4,4,3,4,8,2,1,8,7,2,3,1,7,1,6,9,2,1
1,1,5,6,1,2,8,4,5,2,7,2,3,1,1,7,1,4,8,1,7,8,5,2,2,6,2,1,6,1,1,1,9,1,1,3,6,1,1,6,5,1,4,1,1,1,1,3,5,5,2,7,6,1,3,6,1,3,5,1,8,7,3,8,5,7,2,9,5,2,2,1,3,9,1,5,1,6,9,8,3,7,1,1,1,3,1,2,1,1,9,8,7,6,1,2,5,7,2,1
8,2,3,2,3,3,2,3,3,1,3,1,1,5,9,1,3,1,8,4,3,9,8,2,4,1,1,1,2,1,6,9,6,8,8,3,4,1,4,3,2,1,1,8,9,2,3,1,8,7,7,8,9,7,6,1,6,1,3,3,2,1,2,1,4,2,9,2,4,4,1,5,1,1,7,8,3,8,9,9,5,3,2,2,1,2,8,1,1,2,3,4,4,1,1,1,1,1,1,3
2,3,2,1,9,6,6,8,8,2,4,2,3,1,9,1,1,6,1,1,3,9,3,1,4,5,9,8,3,1,1,4,5,7,1,7,9,9,8,9,1,6,5,1,9,1,2,1,4,7,5,1,1,1,7,4,1,1,8,1,1,4,1,2,9,7,1,7,5,7,5,1,8,1,1,6,9,1,3,2,4,2,3,1,4,2,9,2,9,5,7,5,3,2,4,1,2,9,8,3
5,1,7,6,1,1,8,3,6,5,2,3,1,1,1,3,2,2,8,2,5,3,1,1,2,1,8,9,9,5,7,1,5,9,3,5,1,1,5,8,5,1,3,4,7,3,4,2,8,8,2,4,3,5,9,1,9,9,4,5,7,9,3,2,1,3,7,4,6,9,3,2,9,9,1,5,8,1,2,1,6,9,5,3,1,1,3,3,1,7,6,1,3,1,7,1,5,2,1,1
7,6,5,1,1,3,1,4,5,7,2,2,8,4,9,1,9,8,5,1,2,3,3,3,4,1,2,1,7,9,1,1,4,2,3,1,6,2,2,4,3,4,5,1,4,1,4,1,2,3,8,8,1,3,7,9,2,1,7,4,5,3,6,3,8,1,9,2,1,4,4,2,1,8,1,2,1,2,3,1,2,2,1,1,1,4,1,5,1,7,1,2,1,8,4,2,3,2,1,1
3,4,6,2,3,9,1,9,1,7,2,9,7,9,9,7,8,1,2,1,1,1,3,9,4,3,5,6,2,3,2,3,9,1,7,7,1,4,3,7,3,9,1,4,1,9,1,4,9,4,4,1,4,3,1,3,4,2,3,1,2,8,2,1,3,7,1,5,1,1,3,6,8,7,5,1,4,7,1,1,6,7,1,5,2,8,2,4,4,2,6,2,3,6,1,1,9,2,2,9
4,6,7,3,1,8,5,1,5,2,1,1,2,5,9,2,8,1,9,1,8,1,8,6,5,5,9,1,6,1,3,2,4,9,1,1,9,1,5,4,1,1,2,2,8,2,3,3,7,3,9,1,3,4,2,1,9,2,9,7,9,2,1,1,2,9,2,1,1,2,1,1,4,2,2,1,1,2,1,7,9,5,1,6,5,3,3,9,2,5,3,2,1,2,1,4,6,5,3,4
4,2,3,4,9,5,7,2,1,5,1,1,9,1,1,8,6,2,2,8,5,1,1,2,2,1,2,1,2,8,8,1,8,4,2,1,4,1,1,9,1,2,3,1,5,9,6,7,5,3,8,1,7,8,1,9,2,4,9,2,1,3,9,2,1,3,9,6,5,1,7,3,8,8,6,1,6,4,1,3,2,4,1,3,5,4,4,9,3,1,1,3,8,7,5,2,8,3,4,1
5,2,1,9,6,2,3,9,2,2,5,9,4,3,9,1,3,7,2,9,1,9,2,3,6,7,1,8,3,3,2,1,8,6,1,3,3,2,8,4,1,8,7,9,6,1,8,5,2,8,6,5,7,7,4,3,1,8,2,6,9,2,4,3,6,5,1,8,1,8,1,4,4,1,9,1,5,2,4,9,9,6,1,5,9,1,1,1,3,1,3,2,4,2,9,1,8,4,2,1
7,1,6,3,4,7,3,1,9,2,1,4,9,7,2,5,2,2,1,2,1,2,2,6,1,1,6,1,2,1,1,4,5,1,2,1,2,2,1,3,3,1,2,9,8,9,1,1,1,2,3,3,5,1,4,9,3,3,3,3,1,9,9,1,2,4,3,9,1,3,2,9,1,4,1,1,7,2,6,8,2,8,4,4,2,2,9,5,1,9,2,9,1,8,3,3,6,1,4,1
9,1,2,2,1,2,1,5,2,2,3,4,2,1,5,8,3,5,5,1,1,4,5,9,1,2,2,9,4,1,8,9,5,4,4,1,1,9,2,9,5,8,2,1,3,3,4,6,6,6,7,1,8,1,1,4,2,5,7,2,5,9,8,5,3,1,3,5,1,9,7,9,6,5,4,3,5,1,3,4,5,9,1,8,8,2,2,9,9,9,1,4,1,1,9,1,9,2,1,9
1,7,9,2,3,2,1,4,8,1,1,6,8,1,7,5,5,1,5,5,8,3,2,1,1,9,1,4,3,5,5,1,1,9,4,2,5,2,3,6,1,1,3,4,3,8,2,1,7,2,5,5,8,1,1,3,2,7,5,4,8,8,1,8,5,3,3,4,3,9,1,1,8,1,1,2,2,2,5,6,4,7,9,9,2,4,1,1,8,9,4,3,1,1,2,2,1,9,4,2
6,2,3,5,9,6,1,5,2,1,3,6,2,3,6,2,3,3,1,1,4,6,9,5,7,1,1,8,4,1,7,1,3,4,1,9,5,2,2,1,3,7,2,1,1,5,1,7,4,3,3,3,5,6,2,1,1,4,5,7,7,9,2,1,4,5,3,1,2,5,9,1,5,9,7,6,3,1,7,1,2,9,2,4,8,1,2,6,3,3,1,1,7,6,5,1,4,5,2,2
1,3,1,5,3,2,2,1,7,4,6,5,1,1,1,9,9,2,7,4,1,1,8,5,3,8,6,1,3,1,3,1,1,8,3,1,8,5,2,1,8,5,1,6,3,7,5,1,2,4,1,7,7,7,9,1,7,1,1,4,1,5,4,9,4,6,8,4,9,1,2,1,6,9,1,8,1,5,1,4,7,7,1,9,6,1,2,1,5,8,3,9,8,1,6,3,1,7,5,5
3,9,4,1,5,1,2,4,4,2,3,3,3,1,3,1,7,3,3,9,6,4,9,3,8,1,4,1,1,3,1,3,3,2,1,8,1,1,8,7,1,7,2,1,2,1,9,1,1,1,3,5,9,1,9,7,5,2,6,3,7,3,3,9,8,1,2,9,9,1,5,1,3,2,3,1,4,1,1,2,1,2,5,9,6,2,5,5,6,2,3,6,1,1,1,1,3,5,3,9
4,2,2,1,4,1,1,7,8,3,2,2,1,1,8,1,6,2,2,9,4,8,6,9,2,3,5,1,1,6,4,3,1,2,6,3,9,5,1,1,9,1,1,5,9,2,5,2,1,1,2,8,1,1,9,2,1,1,7,3,9,9,4,1,2,4,4,4,2,7,4,7,1,1,1,1,8,9,2,9,2,5,5,7,1,1,3,1,1,9,2,5,7,3,4,3,9,9,1,9
1,1,7,9,1,9,6,1,1,5,2,1,2,2,5,1,2,6,1,6,2,9,5,1,3,3,1,2,9,9,1,6,1,4,7,9,4,1,6,1,9,8,3,4,4,1,1,1,2,2,5,9,2,6,1,1,3,7,2,5,6,5,1,1,9,1,5,7,2,3,1,1,8,3,1,9,3,3,2,7,3,9,1,4,2,1,5,3,9,2,2,1,2,3,1,4,3,1,1,7
4,2,3,1,7,1,1,3,9,5,2,1,6,2,1,2,8,1,9,8,7,5,4,2,3,8,2,3,2,1,2,7,1,1,1,6,1,1,9,6,1,1,1,8,2,7,5,3,3,2,2,4,9,3,2,1,9,7,9,4,1,8,5,9,7,3,1,1,1,1,4,4,2,8,9,9,6,1,4,5,2,4,4,8,3,2,2,8,5,2,7,6,1,7,3,8,6,3,7,8
3,9,1,8,2,4,6,3,1,7,2,8,3,5,1,5,3,2,9,1,5,8,1,2,9,1,9,7,3,7,4,3,1,1,3,2,1,2,1,1,7,1,4,1,1,1,8,3,2,1,1,7,9,6,7,2,5,4,2,7,2,1,2,2,1,1,6,5,1,8,7,3,1,2,1,3,3,4,1,1,1,7,9,4,8,1,8,2,1,1,4,2,1,1,2,2,4,8,4,7
2,9,2,3,8,1,8,1,4,7,3,5,9,8,1,7,2,6,4,9,2,6,7,1,1,2,1,9,2,3,4,4,8,2,5,9,1,4,9,3,1,3,8,1,5,5,1,4,7,2,5,1,1,1,9,9,1,4,1,2,9,5,6,5,3,9,2,3,9,1,2,7,1,1,7,6,1,1,1,1,3,7,4,7,6,6,8,3,6,2,1,5,4,7,2,1,4,2,1,7
1,9,6,1,3,8,1,3,6,1,7,3,4,2,3,2,1,2,3,8,4,3,9,1,1,2,6,1,2,4,7,1,1,3,6,1,9,3,5,3,5,1,3,9,9,3,3,2,3,2,6,2,5,9,8,1,1,8,1,8,1,1,7,9,5,1,4,3,7,1,4,2,2,8,8,3,5,4,9,9,2,9,2,3,1,3,9,4,5,8,4,1,6,5,2,1,1,8,3,2
8,5,1,4,1,1,1,7,2,2,9,5,1,3,2,6,1,6,2,6,1,3,1,9,1,8,1,3,3,4,6,2,3,1,1,7,2,2,1,4,4,4,1,6,1,8,7,8,1,8,1,8,3,6,2,2,1,3,5,9,7,2,3,5,8,8,4,1,1,4,8,4,1,3,1,6,1,6,9,2,1,9,1,8,2,9,9,5,6,1,2,5,6,3,2,3,3,8,2,1
1,3,6,5,7,3,2,5,4,2,8,3,1,9,6,4,7,3,1,2,1,6,3,1,3,2,7,2,6,1,9,2,8,3,7,2,1,2,4,2,1,7,1,4,5,1,8,1,5,3,5,6,1,2,1,3,3,1,1,1,3,3,1,1,6,2,3,9,8,4,4,3,2,3,5,3,1,1,8,7,2,1,9,3,8,9,1,9,5,6,2,1,9,1,4,5,1,1,1,1
2,8,2,2,9,3,9,3,6,1,3,1,9,1,9,8,1,5,5,1,9,1,3,1,2,1,9,3,2,1,7,3,4,1,7,2,6,1,4,2,2,6,3,4,1,7,9,4,2,3,3,2,1,2,2,2,7,1,8,6,6,6,5,4,3,3,4,5,3,1,1,1,7,1,9,9,7,3,1,4,1,2,1,8,6,2,1,5,3,1,5,1,4,6,8,7,7,9,2,7
1,1,1,1,4,5,4,3,5,9,8,1,3,5,2,4,1,2,3,7,6,1,9,6,9,5,1,5,7,2,9,9,2,2,4,3,7,7,1,1,1,4,7,2,3,5,2,6,5,4,5,1,4,9,2,1,8,3,3,5,2,7,2,3,9,9,2,1,5,6,2,1,4,6,4,3,5,8,4,1,8,2,7,1,1,6,8,2,7,5,4,2,2,6,1,5,1,2,6,3
2,9,7,7,2,3,4,3,3,6,5,5,2,2,5,5,4,6,1,7,9,2,6,3,6,5,5,1,9,1,6,6,7,3,2,1,3,9,2,1,5,6,4,4,3,4,1,2,1,8,4,7,7,3,1,3,5,2,8,1,5,4,7,4,1,5,3,1,5,2,2,1,1,8,5,8,9,2,3,4,9,9,4,3,6,9,8,1,6,2,2,8,2,3,1,4,2,3,4,8
1,2,9,2,1,1,6,1,3,1,5,4,8,4,8,5,8,2,3,1,8,1,1,1,8,5,1,9,8,3,4,2,1,9,2,6,7,1,1,2,9,9,4,5,1,8,1,9,4,9,3,1,1,3,9,2,5,2,1,9,4,5,2,9,1,3,3,1,8,7,3,8,9,4,2,2,5,3,1,7,1,1,1,9,5,2,7,4,9,2,6,6,8,3,5,1,6,3,7,1
4,9,1,1,1,9,1,3,6,1,1,8,8,7,6,6,1,1,3,5,5,2,1,1,5,1,7,2,2,6,5,1,3,8,2,9,3,7,9,1,3,2,1,8,8,9,2,1,2,1,6,9,6,4,5,4,5,1,8,6,9,6,7,1,9,9,1,4,1,2,1,6,1,7,4,8,4,1,6,4,1,2,3,1,2,6,1,2,8,5,6,4,1,1,2,4,3,1,8,6
1,3,1,7,1,7,1,1,7,8,1,8,6,6,4,6,3,2,9,4,4,1,1,5,2,4,2,6,2,2,8,8,1,3,2,6,3,6,6,1,1,9,8,7,2,1,3,2,3,1,2,8,3,4,1,1,1,1,3,2,6,6,1,7,2,1,1,7,2,6,4,9,1,9,3,2,4,7,3,9,2,1,1,2,5,9,1,5,1,1,1,3,8,2,1,6,2,1,9,8
1,1,8,5,1,1,2,1,9,4,7,7,2,9,2,1,8,9,9,8,1,9,1,6,4,2,2,7,5,9,9,2,1,6,3,1,2,8,1,1,9,2,1,6,8,8,1,2,1,2,9,3,7,5,8,4,3,2,6,4,8,2,2,1,1,1,8,3,1,1,6,8,2,1,4,2,2,1,1,8,2,2,2,1,1,4,3,8,8,6,4,2,2,1,1,5,8,1,1,3
4,5,4,2,9,1,3,9,1,4,2,8,1,2,9,1,3,5,1,2,8,3,3,1,3,2,4,9,3,9,1,8,1,6,2,6,7,7,9,8,7,6,1,3,1,1,6,2,2,9,1,4,8,8,4,3,6,9,1,1,3,2,1,8,5,5,3,1,6,5,2,5,6,6,9,7,9,5,7,1,3,2,9,3,3,6,1,1,9,4,2,9,2,5,1,5,5,2,6,1
4,4,9,4,4,3,1,1,4,6,1,2,9,2,1,3,3,5,1,5,3,4,9,2,9,6,1,5,4,1,8,6,1,2,5,2,4,8,1,3,6,8,8,4,2,3,4,3,1,9,3,1,3,9,8,9,1,4,9,7,2,3,1,1,1,5,2,1,4,1,5,1,3,1,5,4,9,8,8,1,1,9,4,1,9,6,1,4,6,7,1,2,5,1,4,9,7,1,1,1
9,6,2,3,7,8,1,2,4,7,2,1,6,3,1,1,6,8,4,1,1,4,8,1,4,2,1,6,2,9,1,2,7,9,4,2,1,1,2,1,1,1,1,1,3,3,3,2,2,1,1,3,4,4,3,3,3,3,2,6,1,5,5,3,6,5,5,1,4,5,2,1,2,1,2,8,3,9,5,7,5,7,1,4,7,1,2,3,4,1,4,3,1,5,5,2,3,2,8,9
5,3,2,1,1,5,8,3,2,1,1,6,9,2,8,8,2,1,1,4,3,2,6,1,1,6,1,7,3,3,9,9,8,9,1,1,5,9,1,5,6,9,9,5,2,2,2,4,8,1,2,3,1,2,4,4,6,8,1,2,3,7,4,1,1,1,2,9,1,6,9,8,1,1,1,3,2,5,1,2,7,9,2,1,2,3,4,2,2,2,6,7,1,8,1,1,9,5,7,2
3,4,7,4,5,6,1,2,1,1,3,7,2,2,2,7,2,1,2,2,4,1,1,3,3,6,9,5,8,1,2,9,3,2,2,3,6,2,3,9,3,5,6,4,3,4,4,9,4,8,4,5,6,1,1,6,1,1,7,1,7,3,1,3,5,9,8,8,1,1,3,5,1,5,7,1,4,5,1,4,5,3,5,1,3,9,9,5,7,1,1,2,1,1,4,3,1,8,3,3
8,1,1,2,8,6,1,2,1,9,1,2,7,1,1,5,3,1,1,3,2,1,9,9,1,2,2,1,1,7,6,2,7,7,5,4,8,7,3,8,4,1,3,7,8,1,7,4,7,4,7,9,9,4,2,7,7,6,1,2,5,1,8,3,3,2,1,2,1,5,5,9,4,8,6,2,1,1,6,1,1,1,7,7,5,1,2,4,6,1,4,1,5,6,1,8,1,1,3,2
4,9,6,2,7,6,1,7,8,6,2,4,2,3,3,6,1,1,4,1,2,5,1,5,1,1,3,2,2,6,6,3,9,1,3,1,6,1,2,5,1,3,4,3,9,5,3,3,6,1,2,1,1,1,1,2,1,6,1,7,4,6,2,5,1,1,1,1,2,3,8,2,1,1,2,2,7,5,5,6,4,3,6,4,1,2,6,1,5,8,8,2,2,3,8,3,3,9,4,1
4,1,9,8,7,9,1,5,3,9,4,1,5,1,3,1,9,3,9,2,1,4,7,1,9,3,5,6,1,4,4,1,1,1,4,6,2,2,9,2,3,8,6,5,1,4,1,2,1,4,2,4,2,1,2,1,9,6,6,3,9,1,3,2,1,5,1,8,6,2,1,2,3,6,3,5,1,3,4,1,8,7,8,1,2,2,7,2,9,9,4,5,3,2,5,5,4,7,1,8
4,5,9,8,2,3,1,1,2,1,3,1,1,6,1,5,6,1,1,9,1,7,1,6,1,8,1,5,2,2,6,9,9,1,2,2,1,4,6,1,1,1,2,1,6,5,2,6,2,1,1,8,2,1,6,4,2,1,2,5,2,5,3,1,1,5,2,3,1,2,2,2,3,2,9,2,4,4,2,1,8,4,4,9,1,3,1,6,8,4,2,3,9,4,2,6,4,4,2,2
6,2,3,9,9,2,2,3,2,1,1,7,7,6,2,7,2,9,3,4,8,9,3,2,2,1,1,5,3,9,5,6,9,6,2,9,7,8,1,7,3,9,3,9,9,1,2,1,8,9,1,3,4,7,1,1,9,7,2,2,1,1,2,1,2,7,1,1,6,5,8,4,1,5,1,4,3,1,2,4,7,9,8,5,5,3,6,2,1,1,9,5,2,1,8,8,4,9,6,9
1,1,2,9,1,1,4,4,2,9,4,4,2,5,4,2,2,5,1,1,4,9,1,3,2,1,6,5,1,1,9,4,2,4,3,8,3,1,1,3,4,1,1,9,2,1,4,7,1,7,5,4,1,2,1,1,2,1,2,1,4,3,1,9,2,3,7,5,2,7,5,8,3,1,9,1,7,3,5,1,4,3,2,1,2,4,6,4,2,1,9,7,3,2,3,9,2,1,1,2
1,6,5,1,2,3,1,7,3,1,8,5,6,5,5,4,1,9,1,8,8,1,1,4,1,1,1,2,4,1,3,4,5,1,2,5,1,1,7,2,2,1,8,3,2,3,2,4,1,2,4,1,6,6,2,9,2,8,1,1,1,7,3,1,2,7,1,5,1,2,8,2,2,1,4,2,1,6,1,7,1,7,2,1,3,1,2,3,1,1,8,6,1,3,6,1,3,9,5,8
4,2,9,8,1,1,2,9,4,7,1,4,5,1,1,8,9,9,9,2,4,1,6,5,8,6,2,4,2,2,2,9,1,1,2,1,2,3,4,8,4,3,2,9,7,2,4,2,4,6,4,2,4,5,1,3,1,2,2,5,5,9,9,1,2,1,1,3,2,5,3,3,3,5,7,1,2,8,6,3,2,4,4,8,1,1,9,9,9,4,4,6,2,8,3,7,4,3,9,2
2,7,6,1,2,1,6,2,2,1,1,1,1,1,9,9,2,9,5,2,1,6,8,3,8,1,2,1,7,3,1,3,3,1,1,6,9,9,9,2,9,1,1,4,2,8,4,8,1,1,9,3,3,1,7,3,1,6,4,5,7,2,1,3,2,2,5,1,2,2,9,9,5,6,1,8,9,1,1,8,6,1,6,1,4,1,8,1,3,3,1,8,1,1,1,5,1,2,4,2
4,1,2,9,3,7,8,1,1,3,4,7,2,8,1,6,1,2,7,4,8,2,4,3,3,6,6,2,8,2,3,5,2,9,8,1,4,7,1,2,1,3,3,4,2,1,6,9,8,1,9,1,2,4,8,1,8,2,3,9,1,9,5,3,1,5,1,3,9,5,2,2,9,1,1,1,9,3,2,9,8,2,4,3,6,8,2,7,8,7,3,3,1,4,5,2,1,1,1,9
1,5,9,1,5,6,1,8,2,2,1,1,2,6,1,9,6,2,3,2,3,1,5,1,9,7,4,2,5,4,2,1,4,9,1,4,1,6,8,9,3,7,6,4,1,4,2,1,6,7,3,8,2,3,3,4,7,3,2,3,1,1,1,1,3,3,2,1,3,9,3,1,6,4,5,1,9,1,3,2,1,9,3,4,1,5,6,1,4,3,8,2,2,1,3,9,7,8,7,4
3,9,2,7,2,5,1,3,7,9,3,1,1,5,8,6,6,7,6,5,3,9,1,2,3,4,4,4,1,4,6,1,9,9,3,1,9,1,3,6,2,7,4,3,5,1,2,9,1,2,1,8,1,4,6,4,2,8,1,3,8,1,1,2,8,1,6,8,1,1,1,1,2,9,9,2,4,5,2,1,5,9,5,4,8,4,8,1,6,1,6,1,1,2,1,5,8,8,1,4
9,4,1,2,1,1,4,2,1,6,6,6,1,1,1,3,7,5,1,1,8,1,2,2,1,2,8,2,1,8,2,4,2,3,1,3,3,3,1,3,6,1,2,4,1,5,1,6,1,1,9,1,2,1,1,3,3,1,5,8,9,2,1,6,1,7,2,4,7,2,3,5,9,9,8,9,4,7,1,9,1,1,1,3,8,1,1,2,6,9,2,4,4,1,9,3,4,1,3,4
2,2,2,3,2,2,5,3,1,3,9,2,5,9,1,2,1,9,1,3,7,1,1,1,9,9,6,2,3,7,1,2,2,9,1,2,2,1,4,3,9,5,3,3,5,9,5,2,3,1,1,9,7,4,6,4,5,2,5,1,6,4,1,2,2,5,2,4,6,5,9,2,6,2,1,1,8,1,7,1,9,1,2,9,9,1,1,2,6,1,9,1,7,6,1,9,6,2,1,7
1,3,4,6,1,5,8,4,1,2,3,8,9,5,1,6,1,3,1,9,1,6,9,9,1,1,5,9,3,2,1,1,7,1,7,2,7,8,9,2,9,6,7,1,3,4,9,3,1,6,8,8,6,6,1,1,3,1,5,1,1,8,3,5,3,9,1,3,2,9,2,8,9,9,2,1,2,8,3,6,9,6,2,3,4,6,7,3,8,1,9,2,6,5,5,8,2,1,7,5
1,5,2,2,4,6,1,8,4,1,1,9,2,5,6,7,4,4,6,6,1,2,3,4,2,1,3,1,2,1,7,4,1,7,1,5,1,6,1,6,6,4,9,9,1,6,3,9,4,6,7,6,9,3,1,4,2,4,3,3,4,1,3,1,6,4,5,2,7,9,3,1,6,1,1,5,8,3,1,1,3,4,2,5,7,1,6,1,4,1,1,1,1,4,3,3,9,3,1,6
2,9,1,8,2,7,1,2,1,2,1,4,3,9,7,5,1,2,3,1,9,1,4,9,2,5,8,9,1,1,1,4,1,5,8,1,6,1,2,2,6,5,8,2,4,7,9,1,1,5,2,2,1,1,4,9,1,1,7,5,1,8,8,9,7,1,3,8,3,6,9,2,3,1,1,9,7,5,2,1,2,1,5,8,3,4,9,2,3,1,6,9,3,4,2,2,2,7,8,3
2,3,3,5,8,2,2,5,6,7,9,1,7,1,2,4,9,8,1,4,6,7,8,9,3,5,6,4,1,9,2,2,1,5,1,5,1,3,5,3,2,9,7,1,2,2,1,2,3,1,2,9,2,1,2,2,6,1,1,2,2,3,1,9,9,6,7,9,1,4,1,1,2,5,8,6,9,2,4,6,1,1,5,1,4,5,8,1,6,2,2,6,7,2,1,2,5,1,7,1
5,2,6,2,4,1,3,5,4,1,8,8,9,8,9,1,1,8,1,9,2,9,9,1,1,3,1,4,1,5,3,2,1,2,7,2,8,7,2,4,2,9,1,8,1,1,8,1,5,6,2,9,4,1,1,3,2,2,2,2,8,1,3,7,3,3,5,5,3,4,2,1,4,3,1,2,9,5,8,1,6,7,3,9,9,3,1,8,1,9,9,3,5,4,5,7,9,9,2,1
9,1,4,9,2,1,9,5,1,1,8,8,5,7,7,6,1,1,9,1,6,3,1,5,2,4,9,2,4,2,7,7,4,4,9,1,1,1,4,1,6,1,3,2,1,1,1,2,1,1,1,4,7,1,5,2,1,2,2,5,1,2,2,9,2,9,1,2,4,1,1,3,7,5,6,6,4,8,8,6,2,5,1,1,4,2,1,3,2,2,3,2,1,2,1,5,1,1,4,8
1,1,8,1,1,5,7,1,1,8,7,2,4,3,1,7,9,1,1,2,1,3,7,1,1,3,5,8,7,1,9,1,8,8,2,6,3,5,7,4,7,6,2,4,9,9,5,6,4,9,2,2,1,4,1,2,1,3,4,6,2,7,4,8,6,1,1,1,7,8,3,7,9,2,2,8,5,2,1,1,7,3,9,5,1,6,9,1,9,2,8,1,5,4,1,5,4,4,1,2
3,2,1,3,2,1,1,5,1,3,6,2,7,2,9,3,8,1,9,4,2,9,1,6,4,2,2,4,2,3,7,1,2,2,9,3,2,2,1,4,8,9,5,4,5,1,4,5,4,6,1,4,2,4,2,6,2,1,3,1,7,5,2,2,4,7,1,1,6,5,1,3,6,3,8,2,2,9,7,2,3,2,6,5,4,7,2,5,1,5,9,1,2,8,3,1,1,1,1,4
4,4,8,4,7,3,2,9,1,2,1,1,4,2,1,1,5,5,3,1,4,9,8,1,1,9,2,1,4,2,1,3,5,1,3,1,3,1,1,9,1,4,1,2,1,9,4,1,4,1,5,7,1,4,3,6,1,9,5,3,2,5,2,2,8,1,1,6,3,9,9,1,1,3,7,6,1,9,1,3,1,1,1,1,1,1,3,7,3,3,1,9,9,1,1,5,2,9,1,3
1,2,6,2,2,7,7,7,3,1,1,6,5,5,4,2,1,1,6,1,1,1,2,8,2,4,7,7,4,1,7,4,2,7,4,6,6,6,1,7,2,6,5,7,1,1,3,2,2,6,7,2,1,1,9,1,7,7,4,5,6,9,3,6,3,2,2,5,3,1,7,1,1,2,4,1,9,3,5,3,1,4,2,8,3,1,1,9,1,1,2,9,3,1,2,7,1,9,3,2
8,2,1,4,4,8,7,1,2,3,4,1,1,4,1,9,9,6,4,1,2,9,1,1,8,1,2,9,2,5,4,2,4,7,9,1,8,4,4,2,8,3,2,1,9,6,3,7,4,1,3,1,8,4,8,2,6,1,3,7,9,8,4,9,4,1,2,8,5,4,1,1,2,6,2,6,2,7,1,5,1,9,9,2,8,5,3,6,3,1,2,3,5,5,1,1,7,3,1,3
1,8,3,2,1,2,3,9,4,9,3,3,8,9,3,1,1,4,5,3,1,3,4,1,1,2,1,1,9,3,1,5,3,7,4,9,6,1,8,1,4,3,1,5,1,1,2,1,9,1,8,2,2,7,9,2,8,4,2,1,1,8,5,9,1,3,1,6,7,6,5,2,3,2,1,1,6,7,1,2,9,5,2,6,4,6,7,7,2,9,4,3,1,1,1,5,1,2,2,8
1,1,1,3,3,3,1,9,5,2,8,1,1,7,4,2,1,1,9,8,7,5,1,9,5,3,1,6,4,4,9,5,9,1,3,1,1,2,6,1,6,1,8,9,1,6,8,2,5,1,1,1,5,1,7,6,3,2,7,1,9,3,9,8,3,1,1,9,1,9,1,4,1,2,9,2,2,1,3,7,2,5,1,4,9,8,1,1,2,1,9,9,1,3,8,1,4,3,1,1
2,1,8,3,4,3,2,2,3,1,2,9,1,1,8,1,1,2,1,6,7,1,9,6,1,9,4,5,2,2,1,6,3,7,2,5,1,3,7,9,1,9,2,2,9,9,9,3,5,3,7,1,3,9,1,1,3,2,6,1,8,7,4,7,1,1,3,1,4,7,5,9,9,9,8,3,1,2,2,7,1,3,3,6,1,3,3,9,1,1,2,8,2,1,3,6,4,3,1,8
1,2,4,1,5,4,9,6,4,2,1,2,9,9,2,3,3,1,8,1,6,2,1,1,2,1,1,3,9,1,5,3,3,7,8,6,1,4,3,2,3,4,1,8,9,9,7,2,1,9,6,8,1,1,6,3,3,2,3,2,1,2,3,2,3,3,7,3,7,1,3,1,1,1,7,2,2,8,5,4,4,4,6,9,3,9,1,2,3,1,1,1,7,5,8,5,2,3,4,6
6,9,4,3,4,2,5,1,4,9,1,2,6,5,6,2,1,6,5,7,3,8,7,4,2,5,3,9,6,2,2,6,6,6,2,2,1,4,2,9,5,7,4,2,2,2,5,2,8,2,9,7,9,9,6,5,1,1,5,6,2,2,1,1,9,1,7,1,2,1,6,9,8,4,9,5,1,8,4,5,2,1,1,9,2,2,1,1,1,2,1,3,9,2,8,9,1,9,2,5
3,9,5,3,9,1,1,9,6,3,2,1,5,8,1,4,1,6,1,2,6,4,1,1,3,9,9,5,5,1,1,6,8,5,5,4,4,2,1,1,7,9,7,1,8,4,3,1,9,2,9,5,1,3,1,4,7,6,8,2,3,1,1,8,1,2,9,1,2,2,1,9,2,8,2,6,6,6,2,4,6,8,1,1,4,5,2,1,1,1,6,3,2,2,4,4,1,1,3,6
6,1,1,6,3,4,6,3,4,5,6,5,1,1,2,1,6,6,4,9,4,1,9,9,1,1,2,1,1,2,1,3,1,1,4,1,3,3,2,8,9,5,1,5,5,2,3,1,4,2,5,6,1,1,3,4,5,7,8,8,9,1,1,6,1,9,4,3,2,7,1,1,8,6,1,9,5,3,3,4,9,1,3,4,8,8,9,8,1,5,2,2,3,1,2,3,5,1,9,4
1,9,5,3,4,4,1,1,9,1,2,4,9,1,6,2,1,8,6,9,5,2,3,2,1,5,9,1,3,6,1,4,1,7,1,6,2,8,5,9,2,2,5,3,1,1,1,2,3,7,2,2,6,3,3,8,5,4,5,3,5,1,5,6,1,2,1,3,2,7,2,1,1,1,2,1,9,1,4,5,1,1,7,3,1,2,4,1,2,4,6,2,7,2,3,4,2,1,1,3
7,1,1,6,5,4,1,2,9,3,1,1,4,6,1,2,1,9,1,1,3,4,5,4,4,2,1,4,8,4,6,9,1,8,5,1,1,1,2,2,3,2,9,1,2,6,1,3,1,8,4,9,2,7,1,2,5,9,3,1,3,5,6,9,4,1,5,5,7,1,1,1,5,1,3,4,1,4,1,8,1,5,2,1,5,3,1,2,1,1,3,8,9,4,8,8,8,1,7,2
2,1,2,9,2,1,2,4,1,4,4,8,8,7,2,2,1,8,2,3,7,2,3,9,8,7,1,1,8,4,7,4,7,5,1,9,4,1,8,8,4,4,4,2,2,2,5,3,1,9,1,8,3,1,6,1,1,1,3,3,8,5,1,1,9,6,7,9,2,1,1,4,2,3,1,7,4,9,2,1,2,2,1,4,1,5,1,1,8,3,1,5,2,9,1,1,2,8,7,8
7,2,9,9,9,7,1,1,4,8,1,1,1,1,3,3,5,2,1,1,3,7,4,7,7,2,1,1,2,9,1,3,9,3,5,3,9,9,8,3,1,4,6,4,7,8,5,1,2,3,5,4,4,5,1,4,3,5,4,1,8,1,1,8,5,9,9,9,3,7,3,5,4,1,9,7,1,1,8,8,1,1,3,5,1,8,2,5,1,2,6,5,6,2,4,7,1,8,3,8
3,2,2,1,7,5,3,1,2,9,2,2,2,9,4,2,9,2,4,1,6,1,1,4,3,5,1,2,6,5,9,4,2,6,8,1,9,1,8,4,8,1,2,4,5,5,2,7,2,9,1,6,7,1,4,6,8,3,1,3,3,4,2,3,1,3,2,1,2,1,1,2,8,5,1,3,1,6,1,6,8,1,6,1,8,5,2,1,2,5,1,8,8,2,3,6,7,1,2,6
7,5,1,4,3,9,5,6,1,3,9,3,3,6,3,4,1,4,1,3,1,2,2,1,1,1,4,5,2,4,3,3,5,5,5,5,3,2,7,1,1,1,7,3,2,2,4,1,7,2,3,2,9,7,2,8,6,2,4,1,1,2,1,1,8,8,1,3,1,2,3,1,1,6,8,4,7,1,4,7,1,8,1,2,7,5,3,9,3,1,4,1,3,1,6,1,3,7,8,1
3,7,5,5,1,6,4,1,8,1,8,8,4,7,3,7,3,4,4,1,5,7,2,4,1,1,9,1,4,4,1,9,1,7,2,8,2,4,3,5,9,8,5,8,7,2,2,6,8,3,6,9,1,2,8,9,1,4,8,7,1,2,1,1,2,4,6,7,8,1,4,8,9,1,6,1,6,1,4,8,2,7,2,7,2,7,3,1,2,1,4,5,5,3,1,4,1,9,1,2
1,2,1,3,1,5,1,3,4,6,8,5,1,1,9,1,5,2,7,1,4,3,9,8,7,9,2,9,9,4,4,8,1,9,1,8,5,1,2,2,1,7,1,1,1,9,4,3,1,9,2,8,5,1,2,7,1,8,3,4,1,1,2,6,5,1,4,3,8,5,3,1,1,2,6,4,4,7,1,6,2,9,2,1,1,1,1,6,1,2,5,4,6,1,4,7,2,1,7,7
7,9,4,5,1,1,9,1,1,1,9,1,9,5,3,5,2,3,4,6,6,2,1,3,2,6,2,1,9,4,4,6,4,1,6,7,3,2,2,1,4,7,1,9,4,4,1,1,8,2,1,2,2,1,6,7,1,2,8,9,1,2,9,7,1,8,2,7,8,3,9,4,4,7,4,4,7,1,1,8,5,9,2,7,1,9,1,9,3,9,5,4,1,1,2,5,8,1,4,2
2,8,3,3,1,2,3,3,1,3,2,9,3,1,9,9,8,4,4,7,1,1,3,1,4,5,2,1,1,9,9,7,1,9,3,6,1,1,9,1,9,3,1,4,3,8,6,6,1,2,2,2,2,1,2,2,2,8,9,9,3,1,1,1,1,1,1,4,9,7,1,1,1,3,9,5,1,2,2,6,2,1,7,1,2,9,7,2,3,7,1,1,3,9,9,3,9,6,1,9
4,3,2,1,2,9,3,4,8,9,6,5,6,6,9,8,5,2,1,6,5,3,2,8,2,4,1,4,2,9,5,1,1,3,1,9,1,9,8,6,2,5,2,7,6,4,5,1,3,9,9,1,5,5,4,3,3,1,5,6,2,2,1,2,6,2,9,4,1,2,6,2,1,4,5,4,1,1,1,1,1,4,2,7,1,5,6,9,2,9,9,3,1,7,7,2,6,1,8,1
3,1,3,1,2,4,1,1,8,9,7,3,1,3,3,5,2,3,1,2,1,4,3,1,9,8,7,2,3,1,1,1,1,9,7,8,9,9,2,1,5,1,2,3,9,2,8,1,6,1,2,3,5,9,7,3,8,7,1,2,8,4,1,2,6,6,7,1,1,9,9,1,5,3,8,6,4,1,4,2,1,7,1,9,5,1,2,9,4,9,2,2,2,1,9,1,3,4,8,2
7,1,3,6,1,3,2,5,1,3,1,3,2,2,8,1,6,3,9,7,1,2,3,1,1,6,1,8,2,3,1,2,1,1,2,6,8,2,9,1,8,3,1,3,1,3,4,2,5,1,2,5,1,8,9,3,2,8,1,6,1,6,8,1,9,9,3,3,5,3,1,1,9,7,1,1,5,1,1,1,9,6,6,3,9,1,1,1,6,2,2,9,6,3,4,4,1,1,8,1
4,5,1,6,3,1,1,1,8,1,5,6,5,1,2,3,2,9,6,1,9,4,7,7,9,6,7,1,4,5,6,3,2,1,6,1,1,3,2,9,6,1,5,3,2,4,4,1,1,3,8,2,7,4,3,4,1,9,1,1,1,2,1,9,9,5,1,2,2,4,1,3,5,4,1,1,3,3,4,6,1,3,1,5,4,1,4,2,1,6,8,7,1,2,9,4,2,5,6,1

//! This test solves first part of https://adventofcode.com/2021/day/23
const std = @import("std");
const Graph = @import("graph.zig").Graph;
const math = std.math;
const Str = []const u8;
const Amphipod = enum {
    A,
    B,
    C,
    D,
};
const hallway_length = 7;
const siderooms = 4;
const sideroom_depth = 2;
const PathType = u4;
const State = struct {
    hallway: [hallway_length]?Amphipod = .{null} ** hallway_length,
    rooms: [siderooms][sideroom_depth]?Amphipod,
    pub fn print(self: @This()) []u8 {
        const blank =
            \\#############
            \\#...........#
            \\###.#.#.#.###
            \\  #.#.#.#.#
            \\  #########
        ;
        var buffer: [100]u8 = undefined;
        var mod: []u8 = buffer[0..blank.len];
        std.mem.copy(u8, mod, blank);
        for (self.hallway) |amp, idx| {
            if (amp != null) {
                const i: usize = switch (idx) {
                    0 => 14 + 1,
                    1 => 14 + 2,
                    2 => 14 + 4,
                    3 => 14 + 6,
                    4 => 14 + 8,
                    5 => 14 + 10,
                    6 => 14 + 11,
                    else => unreachable,
                };
                const a: u8 = switch (amp.?) {
                    .A => 'A',
                    .B => 'B',
                    .C => 'C',
                    .D => 'D',
                };
                mod[i] = a;
            }
        }
        for (self.rooms) |room, rid| {
            for (room) |amp, aid| {
                if (amp != null) {
                    const a: u8 = switch (amp.?) {
                        .A => 'A',
                        .B => 'B',
                        .C => 'C',
                        .D => 'D',
                    };
                    mod[14 + 14 + rid * 2 + 3 + 14 * aid] = a;
                }
            }
        }
        return mod;
    }
    fn sideRoomDone(self: @This(), room: usize) bool {
        std.debug.assert(room < siderooms);
        for (self.rooms[room]) |amp| {
            // https://github.com/ziglang/zig/issues/6059
            if (amp == null) {
                return false;
            } else if (amp != @intToEnum(Amphipod, room)) return false;
        }
        return true;
    }
    fn sideRoomFreeSpace(self: @This(), room: usize) ?u2 {
        var ret: u2 = 0;
        std.debug.assert(room < siderooms);
        for (self.rooms[room]) |amp| {
            if (amp == null) {
                ret += 1;
            } else if (amp != @intToEnum(Amphipod, room)) {
                return null;
            }
        }
        std.debug.assert(ret <= sideroom_depth);
        return ret;
    }
    fn checkSideRoom(self: @This()) ?StateQueue {
        for (self.rooms) |_, idx| {
            const free = self.sideRoomFreeSpace(idx) orelse continue;
            if (free == 0) continue;
            // std.debug.print("FREE: {d}\n", .{free});
            for (self.hallway) |amp, hwidx| {
                if (amp == @intToEnum(Amphipod, idx)) {
                    const steps = (self.checkHWtoRoom(hwidx, idx) orelse continue) + free;
                    var ret: StateQueue = undefined;
                    ret.cost = (std.math.powi(usize, 10, @enumToInt(amp.?)) catch unreachable) * steps;
                    ret.state = self;
                    ret.state.hallway[hwidx] = null;
                    ret.state.rooms[idx][free - 1] = amp;
                    return ret;
                }
            }
            for (self.rooms) |other, oidx| {
                if (idx == oidx) continue;
                var pos: PathType = 0;
                for (other) |amp| {
                    if (amp == null) {
                        pos += 1;
                        continue;
                    }
                    if (amp == @intToEnum(Amphipod, idx)) {
                        var steps: PathType = undefined;
                        if (idx < oidx) { // moving left
                            const hwidx = oidx + 2;
                            // std.debug.print("L->R from: {d} to: {d}\n", .{ hwidx, idx });
                            steps = (self.checkHWtoRoom(hwidx, idx) orelse break) + free + pos;
                        } else { // moving right
                            const hwidx = oidx + 1;
                            // std.debug.print("R->L from: {d} to: {d}\n", .{ hwidx, idx });
                            steps = (self.checkHWtoRoom(hwidx, idx) orelse break) + free + pos;
                        }
                        // we can move amp to his sideroom
                        var ret: StateQueue = undefined;
                        ret.cost = (std.math.powi(usize, 10, @enumToInt(amp.?)) catch unreachable) * steps;
                        ret.state = self;
                        ret.state.rooms[oidx][pos] = null;
                        ret.state.rooms[idx][free - 1] = amp;
                        return ret;
                    }
                    // only first item can move, no need to check others
                    break;
                }
            }
        }
        return null;
    }
    fn checkHWtoRoom(self: @This(), from: usize, to: usize) ?PathType {
        // #############
        // #01.2.3.4.56#
        // ###0#1#2#3###
        //   #0#1#2#3#
        //   #########
        std.debug.assert(to < 4);
        std.debug.assert(from < 8);
        var steps: PathType = 0;
        if (from -| to >= 2) {
            var idx: usize = from -| 1;
            while (idx >= to + 2) : (idx -= 1) {
                // std.debug.print("LEFT from: {d} to: {d} step: {d}\n", .{ from, to, idx });
                if (self.hallway[idx] == null) steps += 2 else return null;
            }
        } else {
            var idx: usize = from + 1;
            while (idx <= to + 1) : (idx += 1) {
                // std.debug.print("RIGHT from: {d} to: {d} step: {d}\n", .{ from, to, idx });
                if (self.hallway[idx] == null) steps += 2 else return null;
            }
        }
        // room entrance point
        if (from != 6 and from != 0) steps += 1;
        return steps;
    }
    pub fn neighborFn(self: @This(), allocator: std.mem.Allocator) ![]StateQueue {
        var ret = std.ArrayList(StateQueue).init(allocator);
        // Amphipod can move to its final place, always a good move
        if (self.checkSideRoom()) |item| {
            try ret.append(item);
            return ret.toOwnedSlice();
        }
        // we already checked the side rooms, so we only have to collect
        // each rooms first item's possible hallway positions
        for (self.rooms) |room, idx| {
            // std.debug.print("ROOM->HW check {d} room\n", .{idx});
            for (room) |amp, pos| {
                if (amp == null) continue;
                // do not move items in right room
                // except: we should move away to let wrong placed amp out
                if (amp == @intToEnum(Amphipod, idx)) {
                    var tainted: bool = false;
                    var next: PathType = @intCast(PathType, pos) + 1;
                    while (next < sideroom_depth) : (next += 1) {
                        if (room[next] != @intToEnum(Amphipod, idx)) tainted = true;
                    }
                    if (!tainted) break;
                }
                for (self.hallway) |hw, hwidx| {
                    if (hw == null) { // destination hallway spot is free
                        // std.debug.print("checking hallway spot {d} with amp {any}\n", .{hwidx, amp});
                        const steps = (self.checkHWtoRoom(hwidx, idx) orelse continue) + pos + 1;
                        var st: StateQueue = undefined;
                        st.cost = steps * try std.math.powi(usize, 10, @enumToInt(amp.?));
                        st.state = self;
                        st.state.hallway[hwidx] = amp;
                        st.state.rooms[idx][pos] = null;
                        try ret.append(st);
                    }
                }
                // only first item can move
                break;
            }
        }
        return ret.toOwnedSlice();
    }
};
fn parseInput(comptime input: Str) !State {
    var lines = std.mem.split(u8, input, "\n");
    var ret = State{ .rooms = undefined };
    var line: usize = 0;
    var counter: usize = 0;
    while (lines.next()) |l| : (line += 1) {
        if (line == 2 or line == 3) {
            for (l) |ch, idx| {
                if (idx == 3 or idx == 5 or idx == 7 or idx == 9) {
                    const amp: Amphipod = switch (ch) {
                        'A' => .A,
                        'B' => .B,
                        'C' => .C,
                        'D' => .D,
                        else => unreachable,
                    };
                    // std.debug.print("{d} {d}\n", .{counter%siderooms, counter/siderooms});
                    ret.rooms[counter % siderooms][counter / siderooms] = amp;
                    counter += 1;
                }
            }
        }
    }
    return ret;
}
const StateQueue = Graph(State).QueueType;
test "Graph" {
    const start_str =
        \\#############
        \\#...........#
        \\###D#D#B#A###
        \\  #B#C#A#C#
        \\  #########
    ;
    const end_str =
        \\#############
        \\#...........#
        \\###A#B#C#D###
        \\  #A#B#C#D#
        \\  #########
    ;
    const start = try parseInput(start_str);
    const end = try parseInput(end_str);
    var solver = Graph(State).init(std.testing.allocator);
    defer solver.deinit();
    const ret = try solver.dijkstra(start, end);
    try std.testing.expectEqual(@as(usize, 16244), ret);
}

const std = @import("std");
const Str = []const u8;
pub fn Graph(comptime T: type) type {
    if (!@hasDecl(T, "neighborFn")) {
        @compileError("Given type (" ++ @typeName(T) ++
            ") must contain a function called `neighborFn`");
    }
    return struct {
        pub const QueueType = struct {
            state: T,
            cost: usize,
        };
        fn lessThan(context: void, a: QueueType, b: QueueType) std.math.Order {
            _ = context;
            if (a.cost == b.cost) {
                return .eq;
            } else if (a.cost < b.cost) {
                return .lt;
            } else {
                return .gt;
            }
        }
        arena: std.heap.ArenaAllocator,
        pub fn init(allocator: std.mem.Allocator) @This() {
            return @This(){
                .arena = std.heap.ArenaAllocator.init(allocator),
            };
        }
        pub fn deinit(self: *@This()) void {
            self.arena.deinit();
        }
        pub fn dijkstra(self: *@This(), start: T, end: T) !usize {
            var visited = std.AutoHashMap(T, void).init(self.arena.allocator());
            defer visited.deinit();
            var queue = std.PriorityQueue(QueueType, void, comptime lessThan)
                .init(self.arena.allocator(), {});
            defer queue.deinit();
            try queue.add(.{ .state = start, .cost = 0 });
            while (queue.count() > 0) {
                const curr = queue.remove();
                if (visited.contains(curr.state)) continue;
                try visited.put(curr.state, {});
                if (std.meta.eql(curr.state, end)) {
                    return curr.cost;
                }
                var nb = try curr.state.neighborFn(self.arena.allocator());
                defer self.arena.allocator().free(nb);
                for (nb) |*n| {
                    n.cost += curr.cost;
                    try queue.add(n.*);
                }
            }
            unreachable;
        }
    };
}

const std = @import("std");
pub fn build(b: *std.build.Builder) void {
    // Standard release options allow the person running `zig build` to select
    // between Debug, ReleaseSafe, ReleaseFast, and ReleaseSmall.
    const mode = b.standardReleaseOptions();
    const lib = b.addStaticLibrary("pathfinder.zig", "src/main.zig");
    lib.setBuildMode(mode);
    lib.install();
    const main_tests = b.addTest("src/main_test.zig");
    main_tests.setBuildMode(mode);
    const test_step = b.step("test", "Run library tests");
    test_step.dependOn(&main_tests.step);
}

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