Problem:
Score : 300 points

Problem Statement

Let f(n) be the number of triples of integers (x,y,z) that satisfy both of the following conditions:

1 \leq x,y,z

x^2 + y^2 + z^2 + xy + yz + zx = n

Given an integer N, find each of f(1),f(2),f(3),\ldots,f(N).

Constraints

All values in input are integers.

1 \leq N \leq 10^4

Input

Input is given from Standard Input in the following format:

N

Output

Print N lines. The i-th line should contain the value f(i).

Sample Input 1

20

Sample Output 1

0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

For n=6, only (1,1,1) satisfies both of the conditions. Thus, f(6) = 1.

For n=11, three triples, (1,1,2), (1,2,1), and (2,1,1), satisfy both of the conditions. Thus, f(6) = 3.

For n=17, three triples, (1,2,2), (2,1,2), and (2,2,1), satisfy both of the conditions. Thus, f(17) = 3.

For n=18, three triples, (1,1,3), (1,3,1), and (3,1,1), satisfy both of the conditions. Thus, f(18) = 3.

Solution in Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;
#[allow(unused_imports)]
use proconio::marker::{Bytes, Chars};
#[allow(unused_imports)]
use std::cmp::{min, max};

fn main() {
	input! {
		nmax: usize,
	}

	let v = vec![
		0,
		0,
		0,
		0,
		0,
		1,
		0,
		0,
		0,
		0,
		3,
		0,
		0,
		0,
		0,
		0,
		3,
		3,
		0,
		0,
		0,
		0,
		0,
		1,
		6,
		0,
		3,
		0,
		0,
		0,
		0,
		0,
		3,
		3,
		6,
		0,
		0,
		3,
		0,
		0,
		0,
		0,
		3,
		3,
		6,
		0,
		6,
		0,
		0,
		0,
		3,
		0,
		0,
		1,
		6,
		0,
		6,
		6,
		0,
		0,
		6,
		0,
		0,
		0,
		0,
		3,
		3,
		3,
		6,
		0,
		6,
		3,
		6,
		0,
		0,
		0,
		6,
		0,
		0,
		0,
		3,
		3,
		9,
		0,
		6,
		3,
		6,
		0,
		3,
		6,
		0,
		0,
		0,
		0,
		6,
		1,
		6,
		0,
		6,
		6,
		0,
		3,
		12,
		0,
		6,
		0,
		0,
		3,
		6,
		0,
		0,
		0,
		3,
		3,
		12,
		0,
		6,
		3,
		6,
		0,
		3,
		6,
		9,
		0,
		6,
		0,
		0,
		0,
		3,
		6,
		3,
		3,
		6,
		0,
		6,
		3,
		12,
		0,
		3,
		6,
		6,
		0,
		6,
		0,
		6,
		3,
		6,
		0,
		0,
		1,
		6,
		3,
		12,
		6,
		0,
		0,
		12,
		0,
		6,
		0,
		6,
		6,
		12,
		0,
		0,
		6,
		0,
		0,
		6,
		0,
		12,
		3,
		6,
		0,
		6,
		3,
		9,
		6,
		3,
		6,
		6,
		0,
		6,
		0,
		6,
		0,
		15,
		6,
		0,
		0,
		6,
		0,
		3,
		3,
		12,
		0,
		12,
		6,
		6,
		0,
		3,
		6,
		6,
		3,
		12,
		0,
		6,
		0,
		9,
		6,
		0,
		0,
		6,
		3,
		12,
		1,
		6,
		6,
		6,
		6,
		0,
		0,
		18,
		0,
		12,
		0,
		3,
		6,
		12,
		0,
		0,
		6,
		3,
		6,
		12,
		0,
		12,
		0,
		0,
		0,
		9,
		3,
		9,
		6,
		12,
		3,
		12,
		0,
		3,
		6,
		6,
		0,
		12,
		0,
		12,
		0,
		9,
		9,
		0,
		0,
		6,
		3,
		6,
		3,
		12,
		6,
		9,
		3,
		6,
		0,
		12,
		3,
		6,
		3,
		9,
		6,
		12,
		6,
		6,
		0,
		6,
		0,
		9,
		6,
		6,
		0,
		12,
		3,
		6,
		0,
		9,
		6,
		6,
		1,
		6,
		0,
		21,
		12,
		6,
		0,
		12,
		0,
		12,
		0,
		0,
		6,
		15,
		6,
		0,
		6,
		12,
		0,
		12,
		0,
		12,
		0,
		0,
		0,
		12,
		0,
		12,
		12,
		3,
		3,
		18,
		3,
		6,
		3,
		6,
		6,
		9,
		9,
		18,
		0,
		6,
		0,
		12,
		0,
		9,
		6,
		0,
		3,
		12,
		3,
		6,
		6,
		12,
		6,
		6,
		0,
		0,
		0,
		15,
		3,
		18,
		3,
		18,
		3,
		12,
		6,
		3,
		6,
		9,
		0,
		12,
		0,
		12,
		0,
		18,
		12,
		0,
		0,
		12,
		3,
		6,
		0,
		6,
		6,
		9,
		6,
		0,
		0,
		18,
		1,
		18,
		3,
		12,
		6,
		6,
		6,
		12,
		0,
		15,
		6,
		12,
		6,
		18,
		0,
		0,
		6,
		0,
		9,
		12,
		0,
		18,
		0,
		6,
		3,
		12,
		0,
		12,
		12,
		0,
		0,
		12,
		0,
		3,
		6,
		12,
		6,
		18,
		9,
		18,
		0,
		9,
		6,
		18,
		0,
		6,
		0,
		6,
		3,
		27,
		6,
		6,
		6,
		6,
		3,
		6,
		0,
		12,
		6,
		9,
		0,
		6,
		0,
		18,
		0,
		9,
		9,
		15,
		3,
		12,
		6,
		6,
		3,
		9,
		6,
		12,
		12,
		18,
		0,
		18,
		0,
		6,
		6,
		21,
		6,
		0,
		0,
		6,
		3,
		15,
		6,
		12,
		6,
		18,
		0,
		0,
		0,
		12,
		6,
		6,
		3,
		6,
		4,
		18,
		6,
		12,
		6,
		3,
		9,
		30,
		0,
		18,
		0,
		6,
		6,
		12,
		6,
		6,
		9,
		12,
		0,
		18,
		6,
		18,
		0,
		6,
		0,
		12,
		0,
		6,
		12,
		6,
		3,
		18,
		0,
		6,
		6,
		6,
		6,
		15,
		3,
		24,
		0,
		6,
		3,
		18,
		0,
		12,
		6,
		12,
		6,
		24,
		0,
		15,
		18,
		9,
		6,
		0,
		0,
		18,
		3,
		6,
		0,
		15,
		12,
		12,
		6,
		6,
		0,
		18,
		0,
		6,
		3,
		12,
		0,
		12,
		6,
		6,
		9,
		9,
		6,
		24,
		3,
		24,
		0,
		9,
		12,
		6,
		6,
		12,
		0,
		12,
		0,
		21,
		9,
		15,
		6,
		12,
		3,
		18,
		3,
		12,
		6,
		12,
		6,
		0,
		0,
		12,
		0,
		12,
		6,
		24,
		0,
		6,
		12,
		6,
		1,
		9,
		6,
		12,
		6,
		24,
		0,
		18,
		3,
		12,
		6,
		6,
		12,
		24,
		0,
		12,
		6,
		15,
		6,
		18,
		0,
		18,
		0,
		0,
		0,
		18,
		9,
		21,
		12,
		0,
		6,
		18,
		0,
		9,
		6,
		6,
		6,
		12,
		0,
		12,
		0,
		9,
		9,
		27,
		6,
		6,
		3,
		18,
		6,
		21,
		6,
		6,
		12,
		12,
		0,
		12,
		0,
		24,
		12,
		0,
		0,
		24,
		3,
		24,
		6,
		12,
		12,
		18,
		0,
		0,
		0,
		12,
		0,
		18,
		3,
		15,
		6,
		12,
		9,
		6,
		0,
		15,
		6,
		9,
		12,
		24,
		0,
		12,
		3,
		6,
		6,
		21,
		6,
		18,
		3,
		18,
		0,
		21,
		12,
		15,
		6,
		6,
		0,
		12,
		3,
		12,
		9,
		18,
		9,
		12,
		6,
		6,
		6,
		24,
		0,
		18,
		3,
		24,
		0,
		6,
		6,
		0,
		6,
		9,
		6,
		6,
		4,
		30,
		0,
		18,
		12,
		9,
		6,
		24,
		0,
		18,
		0,
		9,
		12,
		21,
		6,
		6,
		12,
		12,
		0,
		18,
		0,
		21,
		15,
		12,
		0,
		12,
		6,
		12,
		12,
		18,
		0,
		18,
		0,
		6,
		0,
		9,
		12,
		18,
		6,
		30,
		0,
		0,
		0,
		24,
		6,
		9,
		3,
		12,
		6,
		30,
		3,
		6,
		12,
		6,
		12,
		12,
		0,
		36,
		0,
		6,
		3,
		27,
		12,
		12,
		6,
		6,
		6,
		24,
		0,
		12,
		6,
		12,
		0,
		18,
		0,
		18,
		15,
		18,
		3,
		18,
		6,
		12,
		6,
		6,
		12,
		3,
		6,
		6,
		0,
		12,
		3,
		39,
		3,
		12,
		12,
		12,
		3,
		18,
		0,
		21,
		12,
		21,
		6,
		18,
		0,
		12,
		0,
		9,
		9,
		12,
		9,
		24,
		9,
		12,
		6,
		12,
		6,
		33,
		0,
		6,
		0,
		18,
		0,
		9,
		15,
		12,
		6,
		24,
		6,
		6,
		3,
		15,
		6,
		15,
		12,
		18,
		0,
		18,
		1,
		18,
		6,
		12,
		6,
		6,
		0,
		24,
		6,
		24,
		12,
		18,
		6,
		24,
		0,
		6,
		6,
		12,
		15,
		24,
		0,
		24,
		6,
		6,
		0,
		18,
		0,
		15,
		18,
		12,
		0,
		24,
		0,
		12,
		6,
		12,
		12,
		18,
		6,
		24,
		0,
		0,
		6,
		24,
		3,
		12,
		0,
		12,
		6,
		30,
		9,
		6,
		12,
		24,
		12,
		12,
		0,
		15,
		18,
		12,
		0,
		18,
		0,
		24,
		6,
		15,
		6,
		18,
		3,
		18,
		3,
		12,
		6,
		24,
		12,
		12,
		12,
		6,
		0,
		36,
		0,
		18,
		3,
		6,
		12,
		6,
		9,
		12,
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		3,
		12,
		36,
		0,
		30,
		0,
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		0,
		18,
		6,
		12,
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		24,
		3,
		18,
		12,
		15,
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		24,
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		6,
		18,
		9,
		18,
		12,
		6,
		6,
		24,
		3,
		24,
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		12,
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		12,
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		27,
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		30,
		3,
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		15,
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		12,
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		12,
		24,
		0,
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		6,
		9,
		30,
		9,
		6,
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		21,
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		36,
		6,
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		18,
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		24,
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		6,
		6,
		30,
		6,
		18,
		12,
		9,
		9,
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		30,
		3,
		18,
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		27,
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		30,
		12,
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		12,
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		30,
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		12,
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		30,
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		30,
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		12,
		12,
		18,
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		30,
		6,
		24,
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		6,
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		36,
		12,
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		36,
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		6,
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		24,
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		30,
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		24,
		6,
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		15,
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		12,
		6,
		30,
		9,
		18,
		0,
		42,
		3,
		18,
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		12,
		18,
		33,
		12,
		12,
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		18,
		0,
		21,
		12,
		12,
		12,
		24,
		6,
		30,
		0,
		27,
		18,
		6,
		12,
		6,
		0,
		24,
		0,
		18,
		15,
		30,
		0,
		18,
		12,
		6,
		0,
		21,
		6,
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		24,
		12,
		87,
		27,
		30,
		42,
		24,
		24,
		90,
		0,
		36,
		24,
		60,
		36,
		84,
		0,
		42,
		0,
		30,
		21,
		87,
		12,
		72,
		24,
		42,
		12,
		60,
		30,
		72,
		21,
		60,
		0,
		96,
		12,
		30,
		42,
		39,
		18,
		66,
		12,
		84,
		12,
		63,
		42,
		42,
		24,
		42,
		0,
		18,
		6,
		78,
		15,
		75,
		45,
		54,
		12,
		54,
		6,
		84,
		30,
		30,
		18,
		54,
		0,
		42,
		24,
		39,
		27,
		96,
		18,
		42,
		21,
		48,
		0,
		54,
		18,
		33,
		36,
		66,
		0,
		84,
		0,
		75,
		48,
		30,
		42,
		54,
		12,
		54,
		15,
		42,
		30,
		96,
		18,
		42,
		0,
		18,
		6,
		123,
		15,
		48,
		24,
		48,
		39,
		42,
		6,
		21,
		54,
		45,
		12,
		60,
		0,
		90,
		12,
		30,
		36,
		45,
		18,
		72,
		21,
		78,
		12,
		30,
		12,
		60,
		30,
		18,
		0,
		78,
		6,
		60,
		36,
		33,
		18,
		60,
		12,
		30,
		0,
		60,
		18,
		90,
		30,
		54,
		0,
		36,
		1,
		78,
		27,
		84,
		30,
		18,
		15,
		102,
		9,
		27,
		30,
		24,
		57,
		90,
		0,
		42,
		9,
		48,
		42,
		42,
		12,
		72,
		27,
		48,
		9,
		108,
		18,
		48,
		48,
		18,
		0,
		84,
		6,
		66,
		24,
		48,
		21,
		114,
		6,
		78,
		24,
		30,
		30,
		42,
		18,
		60,
		0,
		18,
		12,
		63,
		9,
		51,
		66,
		48,
		15,
		54,
		0,
		66,
		60,
		36,
		18,
		48,
		0,
		66,
		6,
		36,
		30,
		96,
		9,
		36,
		30,
		30,
		24,
		93,
		24,
		72,
		24,
		66,
		0,
		60,
		24,
		48,
		30,
		24,
		30,
		72,
		6,
		60,
		12,
		30,
		12,
		93,
		18,
		72,
		0,
		30,
		0,
		81,
		30,
		36,
		48,
		36,
		30,
		90,
		6,
		54,
		24,
		57,
		24,
		36,
		0,
		54,
		18,
		36,
		24,
		78,
		18,
		72,
		33,
		12,
		0,
		51,
		30,
		48,
		24,
		42,
		0,
		90,
		3,
		78,
		30,
		30,
		27,
		138,
		6,
		30,
		18,
		36,
		24,
		75,
		24,
		12,
		0,
		54,
		12,
		42,
		18,
		84,
		36,
		30,
		18,
		66,
		6,
		45,
		36,
		36,
		48,
		114,
		0,
		24,
		6,
		30,
		21,
		108,
		15,
		48,
		18,
		36,
		18,
		57,
		24,
		63,
		42,
		54,
		0,
		78,
		6,
		81,
		36,
		18,
		24,
		42,
		18,
		120,
		0,
		24,
		24,
		66,
		12,
		54,
		0,
		48,
		12,
		66,
		18,
		42,
		36,
		48,
		18,
		72,
		6,
		48,
		48,
		33,
		6,
		102,
		0,
		54,
		24,
		39,
		54,
		60,
		12,
		90,
		18,
		36,
		3,
		111,
		24,
		51,
		48,
		42,
		0,
		90,
		0,
		45,
		36,
		54,
		48,
		54,
		24,
		18,
		18,
		51,
		18,
		72,
		0,
		54,
		0,
		18,
		12,
		54,
		36,
		57,
		18,
		42,
		18,
		120,
		0,
		63,
		42,
		27,
		36,
		48,
		0,
		54,
		6,
		39,
		30,
		81,
		18,
		72,
		33,
		54,
		9,
		72,
		12,
		54,
		54,
		24,
		0,
		54,
		15,
		75,
		24,
		60,
		12,
		78,
		6,
		30,
		12,
		39,
		54,
		72,
		6,
		54,
		0,
		72,
		6,
		78,
		12,
		54,
		39,
		30,
		15,
		48,
		6,
		57,
		48,
		18,
		24,
		90,
		0,
		90,
		18,
		42,
		24,
		39,
		42,
		24,
		30,
		42,
		0,
		84,
		6,
		66,
		30,
		30,
		0,
		30,
		0,
		27,
		42,
		39,
		33,
		90,
		24,
		84,
		18,
		51,
		36,
		69,
		24,
		54,
		0,
		42,
		18,
		87,
		33,
		51,
		18,
		42,
		9,
		126,
		9,
		84,
		36,
		66,
		18,
		54,
		0,
		36,
		0,
		66,
		12,
		48,
		15,
		54,
		30,
		18,
		18,
		60,
		18,
		96,
		54,
		42,
		0,
		102,
		0,
		27,
		36,
		30,
		36,
		108,
		15,
		54,
		0,
		24,
		36,
		60,
		24,
		66,
		0,
		30,
		0,
		54,
		15,
		75,
		48,
		36,
		18,
		48,
		24,
		36,
		36,
		54,
		15,
		108,
		0,
		84,
		18,
	];
	for i in 0..nmax {
		println!("{}", v[i]);
	}
}