AT_abc439_b [ABC439B] Happy Number

You are given a positive integer $ N $ . Determine whether $ N $ is a happy number. A happy number is a non-negative integer that becomes $ 1 $ after repeating the following operation a finite number of times: - Replace it with the integer obtained by taking the sum of the squares of the digits in its decimal representation. - For example, performing this operation once on $ 2026 $ replaces it with $ 2^2+0^2+2^2+6^2 = 4+0+4+36 = 44 $ . For examples of happy numbers, refer to the explanations of sample inputs and outputs.

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

If $ N $ is a happy number, output `Yes`; otherwise, output `No`.

### Sample Explanation 1 $ 2026 $ is a happy number. - The digits of $ 2026 $ in decimal representation are $ 2,0,2,6 $ , and taking the sum of their squares gives $ 2^2+0^2+2^2+6^2 = 4+0+4+36 = 44 $ . - The digits of $ 44 $ in decimal representation are $ 4,4 $ , and taking the sum of their squares gives $ 4^2+4^2 = 16+16 = 32 $ . - The digits of $ 32 $ in decimal representation are $ 3,2 $ , and taking the sum of their squares gives $ 3^2+2^2 = 9+4 = 13 $ . - The digits of $ 13 $ in decimal representation are $ 1,3 $ , and taking the sum of their squares gives $ 1^2+3^2 = 1+9 = 10 $ . - The digits of $ 10 $ in decimal representation are $ 1,0 $ , and taking the sum of their squares gives $ 1^2+0^2 = 1+0 = 1 $ . $ 2026 $ is a happy number because it became $ 1 $ after repeating the operation of replacing itself with the integer obtained by taking the sum of the squares of the digits in its decimal representation five times. ### Sample Explanation 2 $ 439 $ is not a happy number. Repeating the operation makes it $ 439 \rightarrow 106 \rightarrow 37 \rightarrow 58 \rightarrow 89 \rightarrow 145 \rightarrow 42 \rightarrow 20 \rightarrow 4 \rightarrow 16 \rightarrow 37 \rightarrow \dotsb $ , and it can be proved that no matter how many times the operation is repeated from here, it will not become $ 1 $ . ### Sample Explanation 3 $ 440 $ is a happy number. ### Constraints - $ N $ is an integer between $ 1 $ and $ 2026 $ , inclusive.