codeforces 766C Mahmoud and a Message(基础dp)

Mahmoud and a Message

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Mahmoud wrote a message s of length n. He wants to send it as a birthday present to his friend Moaz who likes strings. He wrote it on a magical paper but he was surprised because some characters disappeared while writing the string. That's because this magical paper doesn't allow character number i in the English alphabet to be written on it in a string of length more than ai. For example, if a1 = 2 he can't write character 'a' on this paper in a string of length 3 or more. String "aa" is allowed while string "aaa" is not.

Mahmoud decided to split the message into some non-empty substrings so that he can write every substring on an independent magical paper and fulfill the condition. The sum of their lengths should be n and they shouldn't overlap. For example, if a1 = 2 and he wants to send string "aaa", he can split it into "a" and "aa" and use 2 magical papers, or into "a", "a" and "a" and use 3 magical papers. He can't split it into "aa" and "aa" because the sum of their lengths is greater than n. He can split the message into single string if it fulfills the conditions.

A substring of string s is a string that consists of some consecutive characters from string s, strings "ab", "abc" and "b" are substrings of string "abc", while strings "acb" and "ac" are not. Any string is a substring of itself.

While Mahmoud was thinking of how to split the message, Ehab told him that there are many ways to split it. After that Mahmoud asked you three questions:

• How many ways are there to split the string into substrings such that every substring fulfills the condition of the magical paper, the sum of their lengths is n and they don't overlap? Compute the answer modulo 109 + 7.
• What is the maximum length of a substring that can appear in some valid splitting?
• What is the minimum number of substrings the message can be spit in?

Two ways are considered different, if the sets of split positions differ. For example, splitting "aa|a" and "a|aa" are considered different splittings of message "aaa".

Input

The first line contains an integer n (1 ≤ n ≤ 103) denoting the length of the message.

The second line contains the message s of length n that consists of lowercase English letters.

The third line contains 26 integers a1, a2, ..., a26 (1 ≤ ax ≤ 103) — the maximum lengths of substring each letter can appear in.

Output

Print three lines.

In the first line print the number of ways to split the message into substrings and fulfill the conditions mentioned in the problem modulo 109  +  7.

In the second line print the length of the longest substring over all the ways.

In the third line print the minimum number of substrings over all the ways.

Examples

input

3
aab
2 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

output

3
2
2

input

10
abcdeabcde
5 5 5 5 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

output

401
4
3

Note

In the first example the three ways to split the message are:

• a|a|b
• aa|b
• a|ab

The longest substrings are "aa" and "ab" of length 2.

The minimum number of substrings is 2 in "a|ab" or "aa|b".

Notice that "aab" is not a possible splitting because the letter 'a' appears in a substring of length 3, while a1 = 2.

题意：给出一串有小写字母组成的长度为n的字符串。每个小写字母都有对应值ai，分割原串，要求对应值为ai的字符不能出现在长度超过ai的字串中。问共有多少种分割方式，分割后会出现的最长子串长度是多少，采用最少分割次数的方式，最少分割次数是多少？

题解：qaq~~，基础dp都不会，幸亏水了D题，保住了分数。 重点分析第一问吧，后面两问可以直接想到O(n^2)暴力出来的。  我们用dp[i]表示截止到第i个字符的分割次数，最终的dp[n]就是我们要的答案。 在i前面取一个j，如果 [i, j] 可以组成一段子串，那么 dp[i] = dp[i] + dp[j] 

代码如下 ：

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int maxn = 1e3+10;
int dp1[maxn],dp2[maxn],dp3[maxn];
const int INF = 1e9+10;
const int mod = 1e9+7;
char str[maxn];
int cnt[30];
int main()
{
	int n;
	while(scanf("%d",&n)!=EOF)
	{
		scanf("%s",str);
		for(int i=0;i<26;++i)
			scanf("%d",&cnt[i]);
		memset(dp1,0,sizeof(dp1));
		memset(dp2,0,sizeof(dp2));
		memset(dp3,0,sizeof(dp3));
		dp1[0]=1;
		for(int i=1;i<=strlen(str);++i)
		{
			int len=INF;
			dp2[i]=-INF;
			dp3[i]=INF;
			for(int j=i-1;j>=0;--j)
			{
				len=min(len,cnt[str[j]-'a']);
				if(len<i-j)//i到j不能组成一个合法子串 
					break;
				dp1[i]=(dp1[i]+dp1[j])%mod;//截止到第i位的分割方案数 
				dp2[i]=max(dp2[i],max(i-j,dp2[j]));//到第i位可以出现的最长子串 
				dp3[i]=min(dp3[i],dp3[j]+1);//到第i位最小的分割次数 
			}
		}
		printf("%d\n%d\n%d\n",dp1[n],dp2[n],dp3[n]);
	}
	return 0;
}