cf #367(div2) C. Hard problem（DP）

C. Hard problem

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Vasiliy is fond of solving different tasks. Today he found one he wasn't able to solve himself, so he asks you to help.

Vasiliy is given n strings consisting of lowercase English letters. He wants them to be sorted in lexicographical order (as in the dictionary), but he is not allowed to swap any of them. The only operation he is allowed to do is to reverse any of them (first character becomes last, second becomes one before last and so on).

To reverse the i-th string Vasiliy has to spent ci units of energy. He is interested in the minimum amount of energy he has to spent in order to have strings sorted in lexicographical order.

String A is lexicographically smaller than string B if it is shorter than B (|A| < |B|) and is its prefix, or if none of them is a prefix of the other and at the first position where they differ character in A is smaller than the character in B.

For the purpose of this problem, two equal strings nearby do not break the condition of sequence being sorted lexicographically.

Input

The first line of the input contains a single integer n (2 ≤ n ≤ 100 000) — the number of strings.

The second line contains n integers ci (0 ≤ ci ≤ 109), the i-th of them is equal to the amount of energy Vasiliy has to spent in order to reverse the i-th string.

Then follow n lines, each containing a string consisting of lowercase English letters. The total length of these strings doesn't exceed100 000.

Output

If it is impossible to reverse some of the strings such that they will be located in lexicographical order, print  - 1. Otherwise, print the minimum total amount of energy Vasiliy has to spent.

Examples

input

Copy

2
1 2
ba
ac

output

1

input

Copy

3
1 3 1
aa
ba
ac

output

1

input

Copy

2
5 5
bbb
aaa

output

-1

input

Copy

2
3 3
aaa
aa

output

-1

Note

In the second sample one has to reverse string 2 or string 3. To amount of energy required to reverse the string 3 is smaller.

In the third sample, both strings do not change after reverse and they go in the wrong order, so the answer is  - 1.

In the fourth sample, both strings consists of characters 'a' only, but in the sorted order string "aa" should go before string "aaa", thus the answer is  - 1.

题意：给出了N个字符串，要使得字符串按照字典序上升的方式排列，但不能交换两两字符串的位置。唯一允许的操作是翻转该行的字符串，但需要有花费，问使得所有字符串按照上升的方式排列，最少花费为多少。

思路：

参考：

 http://www.cnblogs.com/Sunshine-tcf/p/5793582.html 

因为有翻转和不翻转两种状态，类似01背包，但是还有限制要求要使得字典序上升，所以在状态转移的时候也应该有个限制。

dp[i][0]表示的是第i个字符串不翻转的最少花费，dp[i][1]表示的是第i个字符串翻转的最少花费。

当dp[n][0]和dp[n][1]都为inf则表示无解，输出-1就行，否则输出最小的花费。

代码：

#include 
#include 
#include 
#include 
using namespace std;
typedef long long ll;
const int maxn=100005;
const ll inf=0x3f3f3f3f3f3f3f3f;
string str[maxn];
string rev[maxn];
ll cost[maxn];
ll dp[maxn][2];
int n;
int main()
{
    while(~scanf("%d",&n))
    {
        for(int i=1;i<=n;i++)
        {
            cin>>cost[i];
        }
        for(int i=1;i<=n;i++)
        {
            cin>>str[i];
            rev[i]=str[i];
            reverse(rev[i].begin(),rev[i].end());
        }
        dp[1][0]=0,dp[1][1]=cost[1];
        for(int i=2;i<=n;i++)
        {
            dp[i][0]=inf,dp[i][1]=inf;
            if(str[i]>=str[i-1])
                dp[i][0]=min(dp[i][0],dp[i-1][0]);
            if(str[i]>=rev[i-1])
                dp[i][0]=min(dp[i][0],dp[i-1][1]);
            if(rev[i]>=str[i-1])
                dp[i][1]=min(dp[i][1],dp[i-1][0]+cost[i]);
            if(rev[i]>=rev[i-1])
                dp[i][1]=min(dp[i][1],dp[i-1][1]+cost[i]);
        }
        if(dp[n][0]==inf&&dp[n][1]==inf)
            printf("-1\n");
        else
            printf("%I64d\n",min(dp[n][0],dp[n][1]));
    }
    return 0;
}