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Chef the chief is participating in a hill jumping competition.
There are N hills arranged in a row, and each of them is assigned a unique index from 1 to N — the ith hill has an index Pi on it. The height of the ith hill is Hi.
Chef starts at the first hill with a goal to reach the Nth hill by jumping over hills from left to right (he is not allowed to jump in the other direction), jumping from ith hill to jth costs (Hj - Hi)2 energy.
When chief is on the ith hill, he has to prepare a special dish for the community of that hill as a thanks for letting him use their resources. This will cost him Ai energy (some dishes are chief's favorites and preparing it refreshes chef that why Ai may be negative). To make things more challenging for Chef the chief, he is allowed to jump from ith hill to jth if and only if i < j and Pi < Pj.
Help Chef choose the sequence of jumps that consume the minimum energy possible. (Note that it's possible at any moment that energy consumed is negative.)
The first line of input contains a single integer N.
The second line contains N space-separated integers P1, P2, ... , PN.
The third line contains N space-separated integers A1, A2, ... , AN.
The fourth line contains N space-separated integers H1, H2, ... , HN.
Output a single line containing the answer to the problem i.e. the minimal possible amount of consumed energy.
- 2 ≤ N ≤ 3 × 105
- P is a permutation of the first N integer numbers
- P1=1 and PN=N
- -109 ≤ Ai ≤ 109
- 1 ≤ Hi ≤ 6 × 105
- Subtask 1 (5 points) : 2 ≤ N ≤ 20
- Subtask 2 (15 points) : 2 ≤ N ≤ 5000
- Subtask 3 (20 points) : 2 ≤ N ≤ 3 × 105, Pi = Hi = i
- Subtask 4 (30 points) : 2 ≤ N ≤ 3 × 105, Hi = i
- Subtask 5 (30 points) : original constraints
Input: 5 1 4 3 2 5 0 1 3 0 0 1 2 3 4 5 Output: 10
Example case 1. jumping from first hill to 4th one then to 5th; the answer will be 0 + 0 + 0 + (4-1)^2 + (5-4)^2 = 10
|Tags||convex-hull, dynamic-programming, hard, kingofnumbers, oct15|
|Time Limit:||8 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, SCM chicken, CLOJ, FS|
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