Codeforces gym 101343 J 状压dp

Husam and the Broken Present 2

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

After you helped Husam and rebuilt his beautiful array a he became very happy. To avoid losing his array again, Husam made n copies from it, and distributed it to n of his friends. After that Husam became sure that he can rebuild the array a again if he lost it, so he destroyed the table t.

Today, Husam was looking for his array a, but he was not able to find it. Husam visited all his n friends to take a copy from the array. Unfortunately, all his friends thought that the length of the array a was very long, so instead of keeping the array itself, each friend i take a subarray (li, ri) from the array and kept it in a safe place, and get rid of the rest of the array.

Now Husam has n subarrays from the array a, but he cannot remember the original array or even its length. Husam now needs your help again, he will give you the n subarrays, and your task is to build a new array a such that it contains all the given subarrays inside it as subarrays, and its length must be as minimal as possible. Can you?

Input

The first line contains an integer n (1 ≤ n ≤ 15), where n is the number of friends Husam has.

Then n lines follow, each line i begins with an integer mi (1 ≤ mi ≤ 100), where mi is the length of the subarray the ith friend has. Thenmi integers follow, representing the ith subarray. All values x in the subarrays are in the range (1 ≤ x ≤ 109).

Output

Print the minimal length of the new array a, such that a contains all the given subarrays in the input inside it as subarrays.

Examples

input

3
2 1 2
4 3 4 5 6
3 2 3 4

output

6

input

5
3 4 7 5
4 7 9 2 5
3 7 5 2
4 5 1 4 7
4 9 2 5 1

output

9

Note

A subarray of the array a is a sequence al, al + 1, ..., ar for some integers (l, r) such that (1 ≤ l ≤ r ≤ n).

In the first test case the array a can be [1, 2, 3, 4, 5, 6]. Its length is as minimal as possible, and it contains all the the given subarrays in the input inside it as subarrays.

题意：给你n个序列

构造一个序列  包含这n个子串

输出最小长度

题解：先预处理出任意i子串后面加j子串需要放多少长度  也就是i的后缀和j的前缀重合最大数

然后状压dp

dp[i][j]代表i这个状态下最后面的串为第j个需要的最小长度

然后for一个k搞一搞就可以了

#include
#include
#include
#include
#include
#include
using namespace std;
typedef long long ll;
int a[20][1005],vis[20],cnt,num[20][20],dp[(1<<16)][20];
int main(){
    int n,i,j,k,l;
    scanf("%d",&n);
    for(i=1;i<=n;i++){
        scanf("%d",&a[i][0]);
        for(j=1;j<=a[i][0];j++)scanf("%d",&a[i][j]);
    }
    for(i=1;i<=n;i++){
        for(j=1;j<=n;j++){
            if(i==j||vis[j]||vis[i])continue;
            if(a[i][0]