public int numTilings(int N) {
long[][] dp = new long[N + 1][3];
for (int i = 2; i <= N; i++) {
dp[i][0] = (dp[i - 1][0] + dp[i - 2][0] + dp[i - 1][1] + dp[i - 1][2]) % MOD;
dp[i][1] = (dp[i - 2][0] + dp[i - 1][2]) % MOD;
dp[i][2] = (dp[i - 2][0] + dp[i - 1][1]) % MOD;