Codeforces Round #358 (Div. 2) D. Alyona and Strings

D. Alyona and Strings

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

After returned from forest, Alyona started reading a book. She noticed strings s and t, lengths of which are n and m respectively. As usual, reading bored Alyona and she decided to pay her attention to strings s and t, which she considered very similar.

Alyona has her favourite positive integer k and because she is too small, k does not exceed 10. The girl wants now to choose k disjoint non-empty substrings of string s such that these strings appear as disjoint substrings of string t and in the same order as they do in string s. She is also interested in that their length is maximum possible among all variants.

Formally, Alyona wants to find a sequence of k non-empty strings p₁, p₂, p₃, ..., p_k satisfying following conditions:

• s can be represented as concatenation a₁p₁a₂p₂... a_kp_ka_k + 1, where a₁, a₂, ..., a_k + 1 is a sequence of arbitrary strings (some of them may be possibly empty);
• t can be represented as concatenation b₁p₁b₂p₂... b_kp_kb_k + 1, where b₁, b₂, ..., b_k + 1 is a sequence of arbitrary strings (some of them may be possibly empty);
• sum of the lengths of strings in sequence is maximum possible.

Please help Alyona solve this complicated problem and find at least the sum of the lengths of the strings in a desired sequence.

A substring of a string is a subsequence of consecutive characters of the string.

Input

In the first line of the input three integers n, m, k (1 ≤ n, m ≤ 1000, 1 ≤ k ≤ 10) are given — the length of the string s, the length of the string t and Alyona's favourite number respectively.

The second line of the input contains string s, consisting of lowercase English letters.

The third line of the input contains string t, consisting of lowercase English letters.

Output

In the only line print the only non-negative integer — the sum of the lengths of the strings in a desired sequence.

It is guaranteed, that at least one desired sequence exists.

Examples

Input

3 2 2
abc
ab

Output

2

Input

9 12 4
bbaaababb
abbbabbaaaba

Output

7

Note

The following image describes the answer for the second sample case:

题意：给你两个字符串s，t，他们的长度分别为n,m.要找出一个字符串（s1s2s3s4.....sk）,s1~sk均可以在s，t字符串中找到，且他们在s，t中都是不相交的。

解法：这种题目要求有点类似于求最长公共子串，只不过要加个限制条件间隔的子串不超过k组。我们就可以用dp[i][j][k][0] 表示字符串在i，j这个位置，已经有k组的子串的长度。dp[i][j][k][1]表示i，j，k这种状态下，使用i，j，构成字符串的字符长度

AC：
#include<vector>
 #include <string>
#include <string.h>
#include<stdio.h>
#include<algorithm>
#include<iostream>
#define ll __int64
#include<vector>
using namespace std;
#define maxn 1008
int dp[maxn][maxn][15][2];
int main()
{
    int n, m, k;
    char s1[maxn], s2[maxn];
  scanf("%d%d%d", &n, &m, &k);
  scanf("%s%s", s1+1, s2+1);
  for(int i = 1; i<=m; i++)
 {
    for(int j = 1; j<=n; j++)
    {
      for(int z = 1; z<=k; z++)
      {
        dp[i][j][z][0] = max(dp[i][j-1][z][0], dp[i-1][j][z][0]);
        if(s2[i] == s1[j])    dp[i][j][z][1] = max(dp[i-1][j-1][z][1], dp[i-1][j-1][z-1][0]) + 1;
        dp[i][j][z][0] = max(dp[i][j][z][0], dp[i][j][z][1]);
      }
    }
  }
  printf("%d\n", dp[m][n][k][0]);
  return 0;
}