package q790

const (
	TopHalf int8 = iota
	BottomHalf
	Full

	Modulo int = 1e9 + 7
)

func numTilings(n int) int {
	cache := make([][3]int, n+1)
	cache[0][Full] = 1
	cache[1][Full] = 1

	for w := 2; w <= n; w++ {
		cache[w][Full] = (cache[w-1][Full] + cache[w-2][Full] + cache[w-1][TopHalf] + cache[w-1][BottomHalf]) % Modulo
		cache[w][TopHalf] = (cache[w-1][BottomHalf] + cache[w-2][Full]) % Modulo
		cache[w][BottomHalf] = (cache[w-1][TopHalf] + cache[w-2][Full]) % Modulo
	}
	return cache[n][Full]
}

var _ = numTilings