Kiran is playing a tactical RPG! His signature move is to field a tanky unit, end the turn, and watch all the enemies fail to kill it. He wants to figure out which of his $N$ units is the best tank. Each unit has two corresponding defensive traits: defense and resistance. Defense, represented as $u_i$, mitigates physical attacks. Resistance, represented as $v_i$, mitigates magical attacks. More precisely, the amount of damage a unit takes from a physical attack is $max(\text{Att}-\text{Def},0)$ and the amount of damage a unit takes from a magical attack is $max(\text{Att}-\text{Res},0)$.

In the next battle, Kiran will need his tank to survive against $P$ physical attacks and $M$ magical attacks. The $i^{\text{th}}$ physical attack will have attack stat $a_i$ and the $j^{\text{th}}$ magical attack will have attack stat $b_j$. Help Kiran determine which of his units will take the least total amount of damage.

Constraints

$1\le u_i,v_i,a_i,b_i\le 1000000$
$1\le N,P,M\le 200000$

Input Specification

The first line will contain three space-separated integers, $N$, $P$, $M$.
The next $N$ lines will each contain two space-separated integers, $u_i$ and $v_i$, representing the defense stat and resistance stat of the $i^{\text{th}}$ unit.
The following line will contain $P$ space-separated integers, $a_1,a_2,\dots ,a_P$, representing the physical attacks.
The final line will contain $M$ space-separated integers, $b_1,b_2,\dots ,b_M$, representing the magical attacks.

Output Specification

Output the index of the best tank for the next battle. If there are ties, output the smallest index.

Sample Input 1

3 4 2
40 32
37 29
33 41
33 42 36 39
48 45

Sample Output 1

3

Explanation for Sample 1

Kiran's first unit will take $0+2+0+0=2$ damage from the physical attacks and $16+13=29$ damage from the magical attacks, resulting in $31$ total damage. Kiran's second unit will take $0+5+0+2=7$ damage from the physical attacks and $19+16=35$ damage from the magical attacks, resulting in $42$ total damage. Kiran's third unit will take $0+9+3+6=18$ damage from the physical attacks and $7+4=11$ damage from the magical attacks, resulting in $29$ damage. So Kiran should use his third unit.

Sample Input 2

4 3 3
37 26
37 19
40 24
38 26
51 47 50
62 43 46

Sample Output 2

3

Explanation for Sample 2

The total damage to each unit is $110$, $131$, $107$, and $107$ respectively. There is a tie between the third and fourth unit, so the smaller index, $3$ is the answer.