Problem:
Problem B: Lagrange's Four-Square Theorem

The fact that any positive integer has a representation as the sum of at most four positive
squares (i.e. squares of positive integers) is known as Lagrange’s Four-Square Theorem. The
first published proof of the theorem was given by Joseph-Louis Lagrange in 1770. Your mission
however is not to explain the original proof nor to discover a new proof but to show that the
theorem holds for some specific numbers by counting how many such possible representations
there are.

For a given positive integer n, you should report the number of all representations of n as the
sum of at most four positive squares. The order of addition does not matter, e.g. you should
consider 42 + 32 and 32 + 42 are the same representation.

For example, let’s check the case of 25. This integer has just three representations 12 +22 +22 +42 ,
32 + 42 , and 52 . Thus you should report 3 in this case. Be careful not to count 42 + 32 and
32 + 42 separately.

Input

The input is composed of at most 255 lines, each containing a single positive integer less than
215 , followed by a line containing a single zero. The last line is not a part of the input data.

Output

The output should be composed of lines, each containing a single integer. No other characters
should appear in the output.

The output integer corresponding to the input integer n is the number of all representations
of n as the sum of at most four positive squares.

Sample Input

1
25
2003
211
20007
0

Output for the Sample Input

1
3
48
7
738

Solution in Rust (judge verdict: Accepted)

extern crate core;

use std::fmt;
use std::i32::{MAX};
use std::cmp::{Ordering, min, max };
use std::ops::{Add, Sub, Mul, Div, Neg, Index, IndexMut, SubAssign, Range};
use std::collections::{BTreeMap, VecDeque, BinaryHeap, BTreeSet, HashMap};
use std::fmt::{Display, Formatter, Error};

fn show<T: Display>(vec: &Vec<T>) {
    if vec.is_empty() {
        println!("[]");
    }else {
        print!("[{}", vec[0]);
        for i in 1 .. vec.len() {
            print!(", {}", vec[i]);
        }
        println!("]");
    }
}
fn show2<T: Display>(vec: &Vec<Vec<T>>) {
    if vec.is_empty() {
        println!("[]");
    }else {
        for l in vec {
            show(l);
        }
    }
}
macro_rules! read_lines{
    ($count: expr; $delimiter: expr; $ty: ty) => {{
        let line_count = $count;
        let mut vec: Vec<Vec<$ty>> = Vec::with_capacity(line_count);
        for _ in 0 .. line_count {
            vec.push(read_line!($delimiter; $ty));
        }
        vec
    }};
    ($count: expr; $ty: ty) => {{
        let line_count = $count;
        let mut vec: Vec<$ty> = Vec::with_capacity(line_count);
        for _ in 0 .. line_count {
            vec.push(read_value!());
        }
        vec
    }}
}
macro_rules! read_line{
    () => {{
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).ok();
        line
    }};
    (delimiter: ' ') => {
        read_line!().split_whitespace().map(|x|x.to_string()).collect::<Vec<_>>()
    };
    (delimiter: $p:expr) => {
        read_line!().split($p).map(|x|x.to_string()).collect::<Vec<_>>()
    };
    (' ') => {
        read_line!(delimiter: ' ')
    };
    ($delimiter:expr) => {
        read_line!(delimiter: $delimiter)
    };
    (' '; $ty:ty) => {
        read_line!().split_whitespace().map(|x|x.parse::<$ty>().ok().unwrap()).collect::<Vec<$ty>>()
    };
    ($delimiter:expr; $ty:ty) => {
        read_line!($delimiter).into_iter().map(|x|x.parse::<$ty>().ok().unwrap()).collect::<Vec<$ty>>()
    };
}
macro_rules! read_value{
    () => {
        read_line!().trim().parse().ok().unwrap()
    }
}
macro_rules! let_all {
    ($($n:ident:$t:ty),*) => {
        let line = read_line!(delimiter: ' ');
        let mut iter = line.iter();
        $(let $n:$t = iter.next().unwrap().parse().ok().unwrap();)*
    };
}

macro_rules! let_mut_all {
    ($($n:ident:$t:ty),*) => {
        let line = read_line!(delimiter: ' ');
        let mut iter = line.iter();
        $(let mut $n:$t = iter.next().unwrap().parse().ok().unwrap();)*
    };
}
fn main() {
    let mut count = vec![vec![0; 1 << 15]; 4];
    for n in 1 .. 1 << 8 {
        if n * n >= 1 << 15 {break;}
        count[0][n * n] = 1;
        for c in 0 .. 3 {
            for i in 0 .. (1 << 15) - n * n {
                count[c + 1][i + n * n] += count[c][i];
            }
        }
    }
    loop {
        let_all!(n: usize); if n == 0{break;}
        let mut result = 0;
        for i in 0 .. 4 {
            result += count[i][n];
        }
        println!("{}", result);
    }
}