Linearville

1357
Tempo Limite: 3 | Nível: 5

Descrição

The city of Linearville has N parallel two-way streets going in the West-East direction and N parallel two-way streets going in the South-North direction, making up a
grid with (N − 1) × (N − 1) blocks. The distance between two consecutive parallel streets is either 1 or 5. The Linearville Transit Authority is conducting an experiment and now requires all cars to always follow a path that alternates direction between W-E and S-N at
every crossing, meaning they must turn either left or right when reaching a crossing. The LTA is developing a new navigation app and needs your help to write a program to compute the lengths of shortest alternating paths between many pairs of start and target crossings. The alternating path in the figure, as an example for N = 10, is clearly not a shortest alternating path. But beware! Linearville may be huge.

Entrada

The first line contains an integer N (2 ≤ N ≤ 105) representing the number of streets in each direction. For each direction, the streets are identified by distinct integers from 1 to N starting at the S-W corner of the city. The second line contains N − 1 integers D1 , D2 , . . . , DN −1 (Di ∈ {1, 5} for i = 1, 2, . . . , N − 1) indicating the distances between consecutive streets going S-N (that is, Di is the distance between street i and street i + 1). The third line contains N − 1 integers E1, E2 , . . . , EN −1 (E i ∈ {1, 5} for i = 1, 2, . . . , N − 1) indicating the distances between consecutive streets going W-E (that is, Ei is the distance between street i and street i + 1). The fourth line contains an integer Q (1 ≤ Q ≤ 105) representing the number of shortest path queries. Each of the next Q lines  describes a query with four integers AX , AY , BX and B Y (1 ≤ AX , AY , BX , BY ≤ N ), indicating that the start crossing is (AX , AY ) and the target crossing is (BX , BY ); the values AX and BX are streets going S-N while the values AY and BY are streets going W-E. There are no repeated queries.

Saída

Output Q lines, each line with an integer indicating the length of a shortest alternating path for the corresponding query of the input.


Exemplos de Entrada Exemplos de Saída

5
5 1 5 5
5 1 5 5
2
3 1 4 5
5 5 5 5

23
0

10
5 1 5 5 5 1 1 5 5
1 5 5 5 1 5 5 1 5
3
4 3 9 10
9 2 2 9
5 1 5 10

46
50
49

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Competição: Maratona de Programação da SBC 2017 - Fase Nacional