AT_abc427_b [ABC427B] Sum of Digits Sequence

For a positive integer $ x $ , define $ f(x) $ as the sum of the digits in the decimal representation of $ x $ . For example, $ f(123) = 1 + 2 + 3 = 6 $ . Define an infinite sequence $ A = (A_0, A_1, A_2, \ldots) $ by the following formula: - $ A_0 = 1 $ - For $ i \geq 1 $ , $ A_i = \displaystyle\sum_{j = 0}^{i - 1} f(A_j) $ You are given a positive integer $ N $ . Find the value of $ A_N $ .

The input is given from Standard Input in the following format: > $ N $

Print the answer.

### Sample Explanation 1 - $ A_0 = 1 $ - $ A_1 = f(A_0) = 1 $ - $ A_2 = f(A_0) + f(A_1) = 2 $ - $ A_3 = f(A_0) + f(A_1) + f(A_2) = 4 $ - $ A_4 = f(A_0) + f(A_1) + f(A_2) + f(A_3) = 8 $ - $ A_5 = f(A_0) + f(A_1) + f(A_2) + f(A_3) + f(A_4) = 16 $ - $ A_6 = f(A_0) + f(A_1) + f(A_2) + f(A_3) + f(A_4) + f(A_5) = 23 $ Thus, $ A_6 = 23 $ . ### Constraints - $ N $ is an integer between $ 1 $ and $ 100 $ , inclusive.