PYTRIP3 - Counting Pythagorean Triples


We define a Pythagorean triple as a set of three positive integers $a$, $b$ and $c$ which satisfy $a^2 + b^2 = c^2$.

Let $P(N)$ denote the number of Pythagorean triples whose hypotenuses ($= c$) are less than or equal to $N$ (i.e. $c \le N$).

Given $N$, find $P(N)$.

Input

The first line of input contains a positive integer $N$.

Output

Print on a single line the value of $P(N)$.

Constraints

$1 \le N \le 1234567891011$

Example

Input1:
5

Output1:
1

Input2:
15

Output2:
4

Input3:
10000

Output3:
12471

Input4:
1000000000000

Output4:
4179478903392

Explanation for Input2

There are four Pythagorean triples: $\{3, 4, 5\}$, $\{5, 12, 13\}$, $\{6, 8, 10\}$, $\{9, 12, 15\}$

Information

There are 15 test cases.

The sum of the time limits is 93 sec. (My solution runs in 5.4 sec.)

Source Limit is 5 KB.


hide comments
nguyễn vãn lâm: 2016-01-12 03:19:44

@francky sorry. i was wrong, the problem limited n = 10^4, and i solved it. but my solution cannot apply for above problem

nguyễn vãn lâm: 2016-01-08 08:57:18

oh. unbelievable, spoj world has only 2 people solve this problem. in vietnam, there are 45 people solved successfully. but i'm not in there!

=(Francky)=> Check again constraints !!! And give a try at PYTRIP2 too.

Last edit: 2016-01-13 03:57:07
Szegedi Gábor: 2014-10-19 11:06:29

What faster way there is to generate all primitive triplets than using the Tree of primitive Pythagorean triples?

wisfaq: 2014-10-19 11:06:29

Nice problem!

[Re: Thank you !]

Last edit: 2014-05-30 19:48:16
Min_25: 2014-10-19 11:06:29

@Francky
Thank you. This task is not easy, but the intended solution is relatively simple.

Last edit: 2014-05-26 17:43:26
Francky: 2014-10-19 11:06:29

My "brute force" program took 2h to check sample #4. I need a better approach ; I'll find it ! Thanks for that task.


Added by:Min_25
Date:2014-05-26
Time limit:1s-15s
Source limit:5120B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 GOSU