Codeforces Round #321 (Div. 2) D. Kefa and Dishes 状压DP

D. Kefa and Dishes

 

When Kefa came to the restaurant and sat at a table, the waiter immediately brought him the menu. There were n dishes. Kefa knows that he needs exactly m dishes. But at that, he doesn't want to order the same dish twice to taste as many dishes as possible.

Kefa knows that the i-th dish gives him ai units of satisfaction. But some dishes do not go well together and some dishes go very well together. Kefa set to himself k rules of eating food of the following type — if he eats dish x exactly before dish y (there should be no other dishes between x and y), then his satisfaction level raises by c.

Of course, our parrot wants to get some maximal possible satisfaction from going to the restaurant. Help him in this hard task!

Input

The first line of the input contains three space-separated numbers, n, m and k (1 ≤ m ≤ n ≤ 18, 0 ≤ k ≤ n * (n - 1)) — the number of dishes on the menu, the number of portions Kefa needs to eat to get full and the number of eating rules.

The second line contains n space-separated numbers ai, (0 ≤ ai ≤ 109) — the satisfaction he gets from the i-th dish.

Next k lines contain the rules. The i-th rule is described by the three numbers xi, yi and ci (1 ≤ xi, yi ≤ n, 0 ≤ ci ≤ 109). That means that if you eat dish xi right before dish yi, then the Kefa's satisfaction increases by ci. It is guaranteed that there are no such pairs of indexesi and j (1 ≤ i < j ≤ k), that xi = xj and yi = yj.

Output

In the single line of the output print the maximum satisfaction that Kefa can get from going to the restaurant.

Examples

input

2 2 1
1 1
2 1 1

output

3

 

Note

In the first sample it is best to first eat the second dish, then the first one. Then we get one unit of satisfaction for each dish and plus one more for the rule.

In the second test the fitting sequences of choice are 4 2 1 or 2 1 4. In both cases we get satisfaction 7 for dishes and also, if we fulfill rule 1, we get an additional satisfaction 5.

题意：

　　给你n个菜品，每个菜品有相应的满意度，让你从这n个中选择m个，其中有k个增加满意度的rule

　　x,y,c，表示选择x，y并且x选择在y之前可以获得c的额外满意度

　　问你在选择m个情况下最大的满意度是多少

题解：

　　看到nm的范围就是状态压缩了

　　设定dp[i][j]表示在j状态下前i个物品的最大满意度

　　枚举状态递推就好了

#include <bits/stdc++.h>
using namespace std;
const int N = 20, M = 30005, mod = 1e9 + 7, inf = 0x3f3f3f3f;
typedef long long ll;

ll dp[19][(1<<19)],n,m,k,c[N][N],a[N];
int main() {
    scanf("%I64d%I64d%I64d",&n,&m,&k);
    for(int i=0;i<n;i++) scanf("%I64d",&a[i]);
    for(int i=1;i<=k;i++) {
        ll x,y;
        scanf("%I64d%I64d",&x,&y);
        x--,y--;
        scanf("%I64d",&c[x][y]);
    }
    for(int i=0;i<n;i++) {
        dp[i][(1<<i)] = a[i];
    }
    for(int now=1;now<(1<<n);now++) {
        for(int i=0;i<n;i++) {
            if(!(now&(1<<i))) {
                for(int j=0;j<n;j++) {
                    if(now&(1<<j)) {
                        dp[i][now|(1<<i)] = max( dp[i][now|(1<<i)], dp[j][now]+a[i]+c[j][i]);
                    }
                }
            }
        }
    }
    ll ans = 0;
    for(int i=0;i<(1<<n);i++) {
        int cnt = 0;
        for(int j=0;j<n;j++) if(i&(1<<j)) cnt++;
        if(cnt==m) {
            for(int k=0;k<n;k++) ans=max(ans,dp[k][i]);
        }
    }
    cout<<ans<<endl;
}