private static int part2(char[][] grid) {
    int[][] dp = new int[grid.length][grid[0].length];

    for (int i = 1; i < grid.length; i++) {
        for (int j = 0; j < grid[i].length; j++) {
            char current = grid[i][j];
            char above = grid[i-1][j];

            // If we have the starting point above us, then emit the beam.
            if (above == 'S') {
                grid[i][j] = '|';
                dp[i][j] = 1;
            } else if (current == '^' && above == '|') {
                // If we see a splitter and have a beam above us,
                // then split the beam to the left and right of the splitter.
                if (j-1 >= 0) {
                    grid[i][j-1] = '|';
                    dp[i][j-1] += dp[i-1][j];
                }
                if (j+1 < grid[i].length) {
                    grid[i][j+1] = '|';
                    dp[i][j+1] += dp[i-1][j];
                }
            } else if (above == '|') {
                // If we're on any other spot and have a beam above us, then continue the beam downward.
                grid[i][j] = '|';
                dp[i][j] += dp[i-1][j];
            }
        }
    }

    // Sum up all the unique paths at the bottom of the grid.
    int total = 0;
    for (int i = 0; i < dp[0].length; i++) {
        total += dp[dp.length-1][i];
    }

    return total;
}