Gahui and ILGAM lake

Gahui often visited Konkuk University. Every time Gahui visited Konkuk University, she was surprised to see the huge ILGAM lake. It is bigger than several universities, such as Seokyung university and Hanseong university.

The lake has 4n points arranged like a ring, each numbered from 1 to 4n in counter-clockwise order. Each pair of adjacent points are connected in both directions. In other words:

• If 1 ≤ a < 4n, point a is connected to point a+1 in both directions.
• Point 1 is connected to point 4n in both directions.

Points n, 2n, 3n, and 4n are connected to 3 subway stations (Konkuk_Univ, Guui, Sejong_Univ) via roads. ILGAM lake is so big, the nearest station is different depending on the point. Gahui wants to know which subway station is the nearest to her current point. Please help Gahui.

[Picture 1] Roads and points when n = 2

n is given in the first line.

In the next line, 4n numbers are given in the following format:

d1 d2 ... d4n

• di is distance from point i to point i+1 when 1≤i<4n
• d4n is distance from point 4n to point 1

And the information below is given on four lines.

dn,Konkuk_Univ dn,Guui dn,Sejong_Univ

d2n,Konkuk_Univ d2n,Guui d2n,Sejong_Univ

d3n,Konkuk_Univ d3n,Guui d3n,Sejong_Univ

d4n,Konkuk_Univ d4n,Guui d4n,Sejong_Univ

da,b is the distance between point a and station b.

In the next line, Q (number of questions) is given.

In the next Q lines, Q questions are given in the following format, one per line.

• k
  • What is the distance to the nearest station from point k?

Print the answers to the questions, one per line.

• 1 ≤ all distances in the problem ≤ 105
• 1 ≤ n ≤ 105
• 1 ≤ Q ≤ 105