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 1\,000\,000~
~1 \le N, P, M \le 200\,000~

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.