Codeforces Round #498 (Div. 3) D. Two Strings Swaps

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D. Two Strings Swaps

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given two strings $\mathrm{aa and bb consisting\; of\; lowercase\; English\; letters,\; both\; of\; length nn.\; The\; characters\; of\; both\; strings\; have\; indices\; from 11 to nn,\; inclusive.}$

You are allowed to do the following changes:

• Choose any index $\mathrm{ii (1\le i\le n1\le i\le n)\; and\; swap\; characters aiai and bibi;}$
• Choose any index $\mathrm{ii (1\le i\le n1\le i\le n)\; and\; swap\; characters aiai and an-i+1an-i+1;}$
• Choose any index $\mathrm{ii (1\le i\le n1\le i\le n)\; and\; swap\; characters bibi and bn-i+1bn-i+1.}$

Note that if $\mathrm{nn is\; odd,\; you\; are\; formally\; allowed\; to\; swap a\lceil n2\rceil a\lceil n2\rceil with a\lceil n2\rceil a\lceil n2\rceil (and\; the\; same\; with\; the\; string bb)\; but\; this\; move\; is\; useless.\; Also\; you\; can\; swap\; two\; equal\; characters\; but\; this\; operation\; is\; useless\; as\; well.}$

You have to make these strings equal by applying any number of changes described above, in any order. But it is obvious that it may be impossible to make two strings equal by these swaps.

In one preprocess move you can replace a character in $\mathrm{aa with\; another\; character.\; In\; other\; words,\; in\; a\; single preprocess\; move you\; can\; choose\; any\; index ii (1\le i\le n1\le i\le n),\; any\; character cc and\; set ai:=cai:=c.}$

Your task is to find the minimum number of preprocess moves to apply in such a way that after them you can make strings $\mathrm{aa and bb equal\; by\; applying\; some\; number\; of changes described\; in\; the\; list\; above.}$

Note that the number of changes you make after the preprocess moves does not matter. Also note that you cannot apply preprocess movesto the string $\mathrm{bb or\; make\; any preprocess\; moves after\; the\; first change is\; made.}$

Input

The first line of the input contains one integer $\mathrm{nn (1\le n\le 1051\le n\le 105)\; —\; the\; length\; of\; strings aa and bb.}$

The second line contains the string $\mathrm{aa consisting\; of\; exactly nn lowercase\; English\; letters.}$

The third line contains the string $\mathrm{bb consisting\; of\; exactly nn lowercase\; English\; letters.}$

Output

Print a single integer — the minimum number of preprocess moves to apply before changes, so that it is possible to make the string $\mathrm{aa equal\; to\; string bb with\; a\; sequence\; of changes from\; the\; list\; above.}$

Examples

input

Copy

7
abacaba
bacabaa

output

Copy

4

input

Copy

5
zcabd
dbacz

output

Cop 0

分类讨论太菜了....蛮水的一道题



1 利用Map <char,int> 记录当前位置的字符种类，
1这种情况肯定不用说了
2 这种情况数量可能是 1 3 那么时候利用mp[s[i]]==2就可以判断是不是 1 3 
3 这种情况是 1 1 2 这种情况
这种又分两种情况 那么就是 那么2 实在s1[]还是在 s2[]， 由题意我们可以知道 只能改变s1[]来确保工作可以完成 因此如果2在s1[]的话，我们需要多加ans+=2;
4 ans+=2;

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