if (grid[0] == 0) {
        dp[0][0] = 1;
        dp[0][3] = 1;
    } else {
        dp[0][grid[0]] = 1;
    }
    for (int i = 1; i < n; i++) {
        for (int m = 0; m < 4; m++) {
            if ((m | grid[i]) != m) {
                continue;
            }
            if (m == 0) {
                dp[i][0] = dp[i - 1][0] + dp[i - 1][1] + dp[i - 1][2] + dp[i - 1][3];
                dp[i][0] %= mod;
            } else if (m == 1) {
                if (get_bit(grid[i], 0)) {
                    dp[i][1] = dp[i - 1][0] + dp[i - 1][1] + dp[i - 1][2] + dp[i - 1][3];
                    dp[i][1] %= mod;
                } else {
                    dp[i][1] = dp[i - 1][0] + dp[i - 1][2];
                    dp[i][1] %= mod;
                }
            } else if (m == 2) {
                if (get_bit(grid[i], 1)) {
                    dp[i][2] = dp[i - 1][0] + dp[i - 1][1] + dp[i - 1][2] + dp[i - 1][3];
                    dp[i][2] %= mod;
                } else {
                    dp[i][2] = dp[i - 1][0] + dp[i - 1][1];
                    dp[i][2] %= mod;
                }
            } else {
                if (get_bit(grid[i], 0) + get_bit(grid[i], 1) == 0) {
                    dp[i][3] = dp[i - 1][0] * 2 + dp[i - 1][1] + dp[i - 1][2] + dp[i - 1][3];
                    dp[i][3] %= mod;
                } else if (get_bit(grid[i], 0) == 0 && get_bit(grid[i], 1) == 1) {
                    dp[i][3] = dp[i - 1][0] + dp[i - 1][2];
                    dp[i][3] %= mod;
                } else if (get_bit(grid[i], 0) == 1 && get_bit(grid[i], 1) == 0) {
                    dp[i][3] = dp[i - 1][0] + dp[i - 1][1];
                    dp[i][3] %= mod;
                } else {
                    dp[i][3] = dp[i - 1][0] + dp[i - 1][1] + dp[i - 1][2] + dp[i - 1][3];
                    dp[i][3] %= mod;
                }
            }
        }
    }