CAU 4 30.12.2021

#define task "CAU4"

#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>

using namespace std;

constexpr int N = 1e7 + 5;
int n, cnt[N];
pair<int, int> res[N];

void Read()
{
    cin >> n;
}

void Solve()
{
    int ans(0);

    for (int i = 0; i * i <= n; ++i)
        for (int j = 0; j * j <= n - i * i; ++j)
            ++cnt[i * i + j * j];

    for (int i = 0; i * i <= n; ++i)
        for (int j = 0; j * j <= n - i * i; ++j)
            ans += cnt[n - i * i - j * j];

    cout << ans << "\n";
}

void Additional()
{
    // Ta lấy một cặp số (i, j) đại diện cho (i * i + j * j)
    for (int i = 0; i * i <= n; ++i)
        for (int j = 0; j * j <= n - i * i; ++j)
            res[i * i + j * j] = {i, j};

    int a[4] = {-1, -1, -1, -1};

    // Ta có thể cho rằng i != j => i < j
    for (int i = 0; i * i <= n; ++i)
        for (int j = i + 1; j * j <= n - i * i; ++j)
            if (cnt[n - i * i - j * j])
            {
                a[0] = i;
                a[1] = j;
                a[2] = res[n - i * i - j * j].first;
                a[3] = res[n - i * i - j * j].second;

                goto done;
            }
done:;
    if (a[0] == -1)
    {
        cout << "Vo nghiem";
        return;
    }

    int ans(0);
    do
    {
        for (int i = 0; i < 4; ++i)
            cout << a[i] << " ";
        cout << "\n";
        ++ans;
        if (ans == 4)
            break;
    } while (next_permutation(a, a + 4));
}

int32_t main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    if (fopen(task ".INP", "r"))
    {
        freopen(task ".INP", "r", stdin);
        freopen(task ".OUT", "w", stdout);
    }

    Read();
    Solve();
    Additional();
}