BSPRIME - Binary Sequence of Prime Number

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Binary Sequence of Prime Number is a binary sequence that created by converting prime number to base-2 (Without leading zeros):

(2)10=(10)2
(3)10=(11)2
(5)10=(101)2
(7)10=(111)2
...

If all base-2 of prime number joined, then we get the binary sequence like this: 10111011111011110110...

Now your task is to count how many digit '1' appear in the first N terms of the sequence, example:

-->If N=3, digit '1' appear 2 times: 101110...
-->If N=10, digit '1' appear 8 times: 1011101111101...

Input

The first line is an integer T(1 ≤ T ≤ 50,000), denoting the number of test cases. Then, T test cases follow.

For each test case, there is an integer N(0 ≤ N ≤ 150,000,000) written in one line.

Output

For each test case, output the number of digit '1' appear in the first N terms of the sequence

Example

Input:
3
3
10
50

Output:
2
8
36

 

See also: Another problem added by Tjandra Satria Gunawan


hide comments
nadstratosfer: 2021-03-06 09:28:39

majid, you've hammered so many TLE's, WA's and NZEC's that the 120-submission long SPOJ history doesn't even fully show it, then you switched to CPP and proceeded to hit another 16 WA's and NZEC's before your first AC. I can't even imagine the stupor you find yourself in solving what you consider, as opposed to this, a difficult task, but are you really sure it's the problem that's stupid?

majid: 2021-03-06 08:31:47

I tried 1000000 ways to solve this STUPID problem in CSHARP but TLE after TLE...
I switch to c++ and got ac in 0.32
Actually i think the problem is very very easy and i dont undrestand why there are less than 100 people who solve this STUPID problem.
Try this, it's EASY.

sowmiksarker: 2020-09-25 16:43:34

Finally solved it! Nice problem.

nadstratosfer: 2018-09-04 18:13:22

Unexpected AC with kindof a prototype of a solution. Began thinking about solving this one 3 days ago but didn't like my initial ideas; woke up with better ones and there we go. This is how the best problems work, forcing my brain to work on them even when I don't intend to =)

hodobox: 2017-10-10 21:04:34

I was running out of optimizations, but Eratosthenes barely made it through :P

devendrap: 2016-06-24 15:04:47

Till: 11753933

Last edit: 2016-06-24 15:05:15
vishu: 2015-08-14 16:23:23

@Tjandra Sir can u please tell what improvents can I make in my code or I need to change my brute force approach?
submission id:14891064

Prakhar Gupta: 2014-07-05 06:43:20

any hint???

[Lakshman]: 2014-05-18 18:28:30

Finally Accepted.!!!!!!!!!!

[Lakshman]: 2014-03-30 11:13:57

@Tjandra Satria Gunawan can you please check why I am getting WA, Now I have correct algo with efficient prime computation up to MAX N.


Added by:Tjandra Satria Gunawan
Date:2012-07-12
Time limit:1s
Source limit:10000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM32-GCC ASM64 MAWK BC C-CLANG CPP14 CPP14-CLANG COBOL COFFEE D-CLANG D-DMD DART ELIXIR FANTOM FORTH GOSU GRV 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