CF625D.Finals in arithmetic

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题目描述

Vitya is studying in the third grade. During the last math lesson all the pupils wrote on arithmetic quiz. Vitya is a clever boy, so he managed to finish all the tasks pretty fast and Oksana Fillipovna gave him a new one, that is much harder.

Let's denote a flip operation of an integer as follows: number is considered in decimal notation and then reverted. If there are any leading zeroes afterwards, they are thrown away. For example, if we flip 123123 the result is the integer 321321 , but flipping 130130 we obtain 3131 , and by flipping 3131 we come to 1313 .

Oksana Fillipovna picked some number aa without leading zeroes, and flipped it to get number ara_{r} . Then she summed aa and ara_{r} , and told Vitya the resulting value nn . His goal is to find any valid aa .

As Oksana Fillipovna picked some small integers as aa and ara_{r} , Vitya managed to find the answer pretty fast and became interested in finding some general algorithm to deal with this problem. Now, he wants you to write the program that for given nn finds any aa without leading zeroes, such that a+ar=na+a_{r}=n or determine that such aa doesn't exist.

输入格式

The first line of the input contains a single integer nn ( 1<=n<=101000001<=n<=10^{100000} ).

输出格式

If there is no such positive integer aa without leading zeroes that a+ar=na+a_{r}=n then print 00 . Otherwise, print any valid aa . If there are many possible answers, you are allowed to pick any.

输入输出样例

  • 输入#1

    4
    

    输出#1

    2
    
  • 输入#2

    11
    

    输出#2

    10
    
  • 输入#3

    5
    

    输出#3

    0
    
  • 输入#4

    33
    

    输出#4

    21
    

说明/提示

In the first sample 4=2+24=2+2 , a=2a=2 is the only possibility.

In the second sample 11=10+111=10+1 , a=10a=10 — the only valid solution. Note, that a=01a=01 is incorrect, because aa can't have leading zeroes.

It's easy to check that there is no suitable aa in the third sample.

In the fourth sample 33=30+3=12+2133=30+3=12+21 , so there are three possibilities for aa : a=30a=30 , a=12a=12 , a=21a=21 . Any of these is considered to be correct answer.

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