CodeForces 253D Table with Letters

本文介绍了一种算法,用于计算一个给定的英文字母矩阵中满足特定条件的子矩阵数量。这些条件包括子矩阵中字母'a'的数量不超过k个,并且四个角上的字母必须相同。

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Vasya has recently started to learn English. Now he needs to remember how to write English letters. He isn't sure about some of them, so he decided to train a little.

He found a sheet of squared paper and began writing arbitrary English letters there. In the end Vasya wrote n lines containing m characters each. Thus, he got a rectangular n × m table, each cell of the table contained some English letter. Let's number the table rows from top to bottom with integers from 1 to n, and columns — from left to right with integers from 1 to m.

After that Vasya looked at the resulting rectangular table and wondered, how many subtables are there, that matches both following conditions:

  • the subtable contains at most k cells with "a" letter;
  • all letters, located in all four corner cells of the subtable, are equal.

Formally, a subtable's definition is as follows. It is defined by four integers x1, y1, x2, y2 such that 1 ≤ x1 < x2 ≤ n, 1 ≤ y1 < y2 ≤ m. Then the subtable contains all such cells (x, y) (x is the row number, y is the column number), for which the following inequality holds x1 ≤ x ≤ x2, y1 ≤ y ≤ y2. The corner cells of the table are cells (x1, y1), (x1, y2), (x2, y1), (x2, y2).

Vasya is already too tired after he's been writing letters to a piece of paper. That's why he asks you to count the value he is interested in.

Input

The first line contains three integers n, m, k (2 ≤ n, m ≤ 400; 0 ≤ k ≤ n·m).

Next n lines contain m characters each — the given table. Each character of the table is a lowercase English letter.

Output

Print a single integer — the number of required subtables.

Examples

Input

3 4 4
aabb
baab
baab

Output

2

Input

4 5 1
ababa
ccaca
ccacb
cbabc

Output

1

Note

There are two suitable subtables in the first sample: the first one's upper left corner is cell (2, 2) and lower right corner is cell (3, 3), the second one's upper left corner is cell (2, 1) and lower right corner is cell (3, 4).

#include<map>
#include<vector>
#include<iostream>
#include<queue>
#include<deque>
#include<math.h>
#include<algorithm>
#include<stdio.h>
#include<string>
#include<string.h>
#define ll long long
const int maxn=1e5+10;
using namespace std;
char a[500][500];
int num[500][500];//num[i][j]代表 宽为i 长为j的矩阵中a的数量
int main()
{
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    int n,m,kk;
    scanf("%d%d%d",&n,&m,&kk);
    for(int i=1;i<=n;i++)
        scanf("%s",a[i]+1);
    memset(num,0,sizeof(num));
    for(int i=1;i<=n;i++)
        for(int j=1;j<=m;j++){
          num[i][j]=num[i-1][j]+num[i][j-1]-num[i-1][j-1];
          if(a[i][j]=='a') num[i][j]++;
        }
    ll ans=0;
    int q[300];//选取矩阵中各个字母的出现的对数
    for(int i=1;i<=n;i++)
    {
        for(int j=i+1;j<=n;j++)//枚举矩阵的上边i和下边j
        {
            int p=1;//代表矩阵右边
            memset(q,0,sizeof(q));
            for(int k=1;k<=m;k++)//矩阵左边
            {
                if(a[i][k]!=a[j][k]) continue;//不满足矩形四个点相同
                q[a[i][k]]--;
                while(p<=m&&num[j][p]-num[i-1][p]-num[j][k-1]+num[i-1][k-1]<=kk)
                {
                    if(a[i][p]==a[j][p]) q[a[i][p]]++;
                    p++;//矩形满足a个数小于kk的要求,矩阵右边增大,直到不满足,那么增大左边k++
                }
                if(q[a[i][k]]>0) ans+=q[a[i][k]];//因为矩形左边固定,看右边满足四个点相同条件下有多少个这样的矩形
            }
        }
    }
    printf("%I64d\n",ans);

}

 

### Codeforces 1487D Problem Solution The problem described involves determining the maximum amount of a product that can be created from given quantities of ingredients under an idealized production process. For this specific case on Codeforces with problem number 1487D, while direct details about this exact question are not provided here, similar problems often involve resource allocation or limiting reagent type calculations. For instance, when faced with such constraints-based questions where multiple resources contribute to producing one unit of output but at different ratios, finding the bottleneck becomes crucial. In another context related to crafting items using various materials, it was determined that the formula `min(a[0],a[1],a[2]/2,a[3]/7,a[4]/4)` could represent how these limits interact[^1]. However, applying this directly without knowing specifics like what each array element represents in relation to the actual requirements for creating "philosophical stones" as mentioned would require adjustments based upon the precise conditions outlined within 1487D itself. To solve or discuss solutions effectively regarding Codeforces' challenge numbered 1487D: - Carefully read through all aspects presented by the contest organizers. - Identify which ingredient or component acts as the primary constraint towards achieving full capacity utilization. - Implement logic reflecting those relationships accurately; typically involving loops, conditionals, and possibly dynamic programming depending on complexity level required beyond simple minimum value determination across adjusted inputs. ```cpp #include <iostream> #include <vector> using namespace std; int main() { int n; cin >> n; vector<long long> a(n); for(int i=0;i<n;++i){ cin>>a[i]; } // Assuming indices correspond appropriately per problem statement's ratio requirement cout << min({a[0], a[1], a[2]/2LL, a[3]/7LL, a[4]/4LL}) << endl; } ``` --related questions-- 1. How does identifying bottlenecks help optimize algorithms solving constrained optimization problems? 2. What strategies should contestants adopt when translating mathematical formulas into code during competitive coding events? 3. Can you explain why understanding input-output relations is critical before implementing any algorithmic approach? 4. In what ways do prefix-suffix-middle frameworks enhance model training efficiency outside of just tokenization improvements? 5. Why might adjusting sample proportions specifically benefit models designed for tasks requiring both strong linguistic comprehension alongside logical reasoning skills?
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