package q840

func checkSquare(x, y int, grid [][]int) bool {
	seen := uint16(0)
	rowSum, colSum := [3]int{}, [3]int{}
	diag1sum, diag2sum := 0, 0

	for ty := range 3 {
		for tx := range 3 {
			num := grid[y+ty][x+tx]
			if num < 1 || num > 9 {
				return false
			}
			tSeen := seen | (1 << (num - 1))
			if tSeen == seen { // duplicate number
				return false
			}
			seen = tSeen

			rowSum[ty] += num
			colSum[tx] += num
			if tx == ty {
				diag1sum += num
			}
			if tx+ty == 2 {
				diag2sum += num
			}
		}
	}

	if diag1sum != diag2sum {
		return false
	}
	for i := range 3 {
		if rowSum[i] != diag1sum || colSum[i] != diag1sum {
			return false
		}
	}
	return true
}

func numMagicSquaresInside(grid [][]int) int {
	if len(grid) < 3 || len(grid[0]) < 3 {
		return 0
	}
	w, h := len(grid[0]), len(grid)

	count := 0
	for y := range h - 2 {
		for x := range w - 2 {
			if grid[y+1][x+1] != 5 { // the center cell has to be 5
				continue
			}
			if checkSquare(x, y, grid) {
				count++
			}
		}
	}

	return count
}

var _ = numMagicSquaresInside