Problem:
Score : 200 points

Problem Statement

You are visiting a large electronics store to buy a refrigerator and a microwave.

The store sells A kinds of refrigerators and B kinds of microwaves. The i-th refrigerator ( 1 \le i \le A ) is sold at a_i yen (the currency of Japan), and the j-th microwave ( 1 \le j \le B ) is sold at b_j yen.

You have M discount tickets. With the i-th ticket ( 1 \le i \le M ), you can get a discount of c_i yen from the total price when buying the x_i-th refrigerator and the y_i-th microwave together. Only one ticket can be used at a time.

You are planning to buy one refrigerator and one microwave. Find the minimum amount of money required.

Constraints

All values in input are integers.

1 \le A \le 10^5

1 \le B \le 10^5

1 \le M \le 10^5

1 \le a_i , b_i , c_i \le 10^5

1 \le x_i \le A

1 \le y_i \le B

c_i \le a_{x_i} + b_{y_i}

Input

Input is given from Standard Input in the following format:

A B M
a_1 a_2 ... a_A
b_1 b_2 ... b_B
x_1 y_1 c_1
\vdots
x_M y_M c_M

Output

Print the answer.

Sample Input 1

2 3 1
3 3
3 3 3
1 2 1

Sample Output 1

5

With the ticket, you can get the 1-st refrigerator and the 2-nd microwave for 3+3-1=5 yen.

Sample Input 2

1 1 2
10
10
1 1 5
1 1 10

Sample Output 2

10

Note that you cannot use more than one ticket at a time.

Sample Input 3

2 2 1
3 5
3 5
2 2 2

Sample Output 3

6

You can get the 1-st refrigerator and the 1-st microwave for 6 yen, which is the minimum amount to pay in this case.
Note that using a ticket is optional.

Solution in C (GCC 5.4.1) (judge verdict: Runtime Error)

#include<stdio.h>
#include<string.h>

int main(void){
  int i=0;
  int rei = 0;
  int densi = 0;
  int m = 0;
  scanf("%d", &rei);
  scanf("%d", &densi);
  scanf("%d", &m);
  int rprice[rei];
  int dprice[densi];
  int waribiki[rei][densi];
  int a;
  int b;
  int c;
  for(i=0;i<rei;i++){
    scanf("%d", &rprice[i]);
    //printf("%d", rprice[i]);
  }
  for(i=0;i<densi;i++){
    scanf("%d", &dprice[i]);
    //printf("%d", dprice[i]);
  }
  int j = 0;
  for(i=0;i<rei;i++){
    for(j=0;j<densi;j++){
      waribiki[i][j] = 0;
    }
  }
  for(i=0;i<m;i++){
    scanf("%d", &a);
    scanf("%d", &b);
    scanf("%d", &c);
    //printf("%d", a);
    //printf("%d", b);
    //printf("%d", c);
    //if(waribiki[a-1][b-1] < c){
    	//waribiki[a-1][b-1] = c;
    //}
  }
  int min = 100000;
  int p = 0;
  for(i=0;i<rei;i++){
    for(j=0;j<densi;j++){
      //printf("%d", waribiki[i][j]);
      p = rprice[i] + dprice[j] - waribiki[i][j];
      //printf("%d", p);
      if(p < min){
        min = p;    
      }
    }
  }
  printf("%d", min);
  return 0;
}