{"trustable":false,"sections":[{"title":"","value":{"format":"HTML","content":"\u003ch2\u003e Problem J: Summing Digits\u003c/h2\u003e \n\u003cp\u003e \u003cimg align\u003d\"right\" src\u003d\"http://uva.onlinejudge.org/external/113/p11332.png\" /\u003e\u003c/p\u003e \n\u003cp\u003e For a positive integer \u003ccode\u003en\u003c/code\u003e, let \u003ccode\u003ef(n)\u003c/code\u003e denote the sum of the digits of \u003ccode\u003en\u003c/code\u003e when represented in base 10. It is easy to see that the sequence of numbers \u003ccode\u003en, f(n), f(f(n)), f(f(f(n))), ...\u003c/code\u003e eventually becomes a single digit number that repeats forever. Let this single digit be denoted \u003ccode\u003eg(n)\u003c/code\u003e.\u003c/p\u003e \n\u003cp\u003e For example, consider \u003ccode\u003en \u003d 1234567892\u003c/code\u003e. Then:\u003c/p\u003e \n\u003cpre\u003e\r\nf(n) \u003d 1+2+3+4+5+6+7+8+9+2 \u003d 47\r\nf(f(n)) \u003d 4+7 \u003d 11\r\nf(f(f(n))) \u003d 1+1 \u003d 2\r\n\u003c/pre\u003e \n\u003cp\u003e Therefore, \u003ccode\u003eg(1234567892) \u003d 2\u003c/code\u003e.\u003c/p\u003e \n\u003cp\u003e Each line of input contains a single positive integer \u003ccode\u003en\u003c/code\u003e at most 2,000,000,000. For each such integer, you are to output a single line containing \u003ccode\u003eg(n)\u003c/code\u003e. Input is terminated by \u003ccode\u003en \u003d 0\u003c/code\u003e which should not be processed.\u003c/p\u003e \n\u003ch3\u003e Sample input\u003c/h3\u003e \n\u003cpre\u003e\r\n2\r\n11\r\n47\r\n1234567892\r\n0\r\n\u003c/pre\u003e \n\u003ch3\u003e Output for sample input\u003c/h3\u003e \n\u003cpre\u003e\r\n2\r\n2\r\n2\r\n2\r\n\u003c/pre\u003e"}}]}