Hex Dyslexia

题意翻译

给定一个十六进制数，已知他是两个数 $a, b$ 的差，且 $a$ 在十六进制下的数位经过重新排列可以得到 $b$ 的十六进制表示。 求最小的 $b$。 输入长度 $\leq 14$。

题目描述

Copying large hexadecimal (base 16) strings by hand can be error prone, but that doesn't stop people from doing it. You've discovered a bug in the code that was likely caused by someone making a mistake when copying such a string. You suspect that whoever copied the string did not change any of the digits in the string, nor the length of the string, but may have permuted the digits arbitrarily. For example, if the original string was $ 0abc $ they may have changed it to $ a0cb $ or $ 0bca $ , but not $ abc $ or $ 0abb $ . Unfortunately you don't have access to the original string nor the copied string, but you do know the length of the strings and their numerical absolute difference. You will be given this difference as a hexadecimal string $ S $ , which has been zero-extended to be equal in length to the original and copied strings. Determine the smallest possible numerical value of the original string.

输入输出格式

输入格式

Input will contain a hexadecimal string $ S $ consisting only of digits $ 0 $ to $ 9 $ and lowercase English letters from $ a $ to $ f $ , with length at most $ 14 $ . At least one of the characters is non-zero.

输出格式

If it is not possible, print "NO" (without quotes). Otherwise, print the lowercase hexadecimal string corresponding to the smallest possible numerical value, including any necessary leading zeros for the length to be correct.

输入输出样例

输入样例 #1

f1e

输出样例 #1

NO

输入样例 #2

0f1e

输出样例 #2

00f1

输入样例 #3

12d2c

输出样例 #3

00314

说明

The numerical value of a hexadecimal string is computed by multiplying each digit by successive powers of $ 16 $ , starting with the rightmost digit, which is multiplied by $ 16^{0} $ . Hexadecimal digits representing values greater than $ 9 $ are represented by letters: $ a=10,b=11,c=12,d=13,e=14,f=15 $ . For example, the numerical value of $ 0f1e $ is $ 0·16^{3}+15·16^{2}+1·16^{1}+14·16^{0}=3870 $ , the numerical value of $ 00f1 $ is $ 0·16^{3}+0·16^{2}+15·16^{1}+1·16^{0}=241 $ , and the numerical value of $ 100f $ is $ 1·16^{3}+0·16^{2}+0·16^{1}+15·16^{0}=4111 $ . Since $ 3870+241=4111 $ and $ 00f1 $ is a permutation of $ 100f $ , $ 00f1 $ is a valid answer to the second test case.