Welcome To SDIBT ACM-ICPC Online Judge

VIRTUAL JUDGE Recent Contest F.A.Qs Discuss Home ProblemSet Status Ranklist 4 Contest LoginRegister Exam
Problem 1067. -- Smith Numbers

Smith Numbers

Time Limit: 1 Sec  Memory Limit: 64 MB
Submit: 27  Solved: 10
[Submit][Status][Discuss]

Description

Smith Numbers While skimming his phone directory in 1982, mathematician Albert Wilansky noticed that the telephone number of his brother-in-law H. Smith had the following peculiar property: The sum of the digits of that number was equal to the sum of the digits of the prime factors of that number. Got it? Smith's telephone number was 493-7775. This number can be written as the product of its prime factors in the following way: 4937775 = 3 . 5 . 5 . 65837 The sum of all digits of the telephone number is 4 + 9 + 3 + 7 + 7 + 7 + 5 = 42, and the sum of the digits of its prime factors is equally 3 + 5 + 5 + 6 + 5 + 8 + 3 + 7 = 42. Wilansky named this type of number after his brother-in-law: the Smith numbers. As this property is true for every prime number, Wilansky excluded them from the definition. Other Smith numbers include 6,036 and 9,985. Wilansky was not able to find a Smith number which was larger than the telephone number of his brother-in-law. Can you help him out?

Input

The input consists of several test cases, the number of which you are given in the first line of the input. Each test case consists of one line containing a single positive integer smaller than 109.

Output

For every input value n, compute the smallest Smith number which is larger than n and print it on a single line. You can assume that such a number exists.

Sample Input

1
4937774

Sample Output

4937775

HINT

Source

Mid-Central European Regional Contest 2000

[Submit][Status][Discuss]

HOME Back

한국어 中文 English
All Copyright Reserved 2008-2010 SDIBT TEAM
GPL2.0 2003-2010 HUSTOJ Project TEAM
Anything about the Problems, Please Contact Admin:admin