package q1895

func isMagicSq(grid [][]int, x, y, w int) bool {
	diag1Sum := 0
	diag2Sum := 0
	for i := range w {
		ax, ay := x+i, y+i
		diag1Sum += grid[ay][ax]
		ax = x + w - 1 - i
		diag2Sum += grid[ay][ax]
	}
	if diag1Sum != diag2Sum {
		return false
	}

	// horizontal
	for dy := range w {
		sum := 0
		for dx := range w {
			sum += grid[y+dy][x+dx]
		}
		if sum != diag1Sum {
			return false
		}
	}
	// vertical
	for dx := range w {
		sum := 0
		for dy := range w {
			sum += grid[y+dy][x+dx]
		}
		if sum != diag1Sum {
			return false
		}
	}

	return true
}

func largestMagicSquare(grid [][]int) int {
	k := 1
	gW, gH := len(grid[0]), len(grid)

Outer:
	for w := 2; w <= min(gW, gH); w++ {
		for y := range gH - w + 1 {
			for x := range gW - w + 1 {
				if isMagicSq(grid, x, y, w) {
					k = w
					continue Outer
				}

			}
		}
	}
	return k
}

var _ = largestMagicSquare