## DCEPC501 - Save Thy Toys

Leonard is very fond of buying rare and expensive science fiction toys. He keeps his collection in a sequential order of the date on which the toy was bought in a special closet so that his roomie Sheldon never gets hold of his toys. But because of his bad luck Leonard once loses a bet to Sheldon and Sheldon demands a share Leonard’s toys. Since Leonard doesn’t want to loose much money, he decides upon a strategy to reduce his loss to minimum.

Leonard, beginning from the first toy in his closet will pick some toys, say "x" toys in sequence. Sheldon will then pick the next "x" toys (Note that Sheldon picks equal no. of toys as picked by Leonard in his move unless the remaining toys are less than "x". In that case he picks all of the remaining). This will keep going on till no more toys are left in the closet for Leonard to pick. You are given the sequence of toys with their price. Help Leonard in maximizing the total price of all toys he picks.

Leonard in his each turn can either pick only 1 or 2 or 3 toys ("x" described above can take value either 1, 2 or 3).

### Input

First line specifies T, the number of test cases.

Each test case contains N in the first line. Second line contains N integers as described above.

### Output

Output 1 line for each test case giving the maximum possible value of the total sum of all toys Leonard picks.

### Constraints

1<=T<=10

1<=N<=100000

1<=Price of toys<=1000000

### Example

```Input:
2
4
5 4 3 2
6
10 8 7 11 15 20

Output:
12
53```

Explanation:

In 1st case, Leonard picks 3 toys in his first move with value 5,4,3 and Sheldon has no choice but to pick the last.
In 2nd case, Leonard picks 10, 8. Then Sheldon picks 7,11. And then Leonard picks the rest.

hide comments
 < Previous 1 2 3 4 5 6 7 Next > manjeet_: 2018-08-09 18:44:34 if getting WA .. try using scanf printf and long long int...got accepted in 2nd go karan_yadav: 2018-07-05 14:16:57 Simple recursion with a 1D array for memoization and std::ios::sync_with_stdio(false) will do. 0.13s Though remember to use long long, cost me a WA. priyanshu_98: 2018-06-08 21:37:33 Read carefully the line-Leonard in his each turn can either pick only 1 or 2 or 3 toys ("x" described above can take value either 1, 2 or 3).In each turn he can choose 1 or two or three toys.so x in not fixed.In each move you can change the value of x. Last edit: 2018-06-08 21:38:48 Jas R Mehta: 2018-01-23 13:04:27 use scanf printf instead of cin cout or u will get TLE atikahamedutso: 2017-12-24 09:49:50 finally got AC :) burninggoku: 2017-09-20 10:40:21 AC in one go gives me more happiness :) :) :) than my girlfriend can ever give me... sad part is i am single :( :( mudra03: 2017-09-19 21:28:29 java users TLE :( AC with cpp mastik5h_1998: 2017-09-19 07:39:16 too much optimisation..... :( rohit9934: 2017-08-28 12:40:58 brute force + optimisation = DP lord_poseidon: 2017-08-17 15:32:33 My 100th question

 Added by: dce coders Date: 2012-04-18 Time limit: 0.310s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: ASM32-GCC MAWK BC C-CLANG C CPP C++ 4.3.2 CPP14-CLANG CPP14 COBOL COFFEE D-DMD D-CLANG DART ELIXIR FANTOM FORTH GOSU GRV JAVA JS-MONKEY KTLN NIM NODEJS OBJC OBJC-CLANG OCT PICO PROLOG PYPY PY_NBC R RACKET RUST CHICKEN SQLITE SWIFT UNLAMBDA VB.NET Resource: Own Problem