#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
typedef pair<ll, ll> p_ll;

template<class T>
void debug(T itr1, T itr2) { auto now = itr1; while(now<itr2) { cout << *now << " "; now++; } cout << endl; }
#define repr(i,from,to) for (ll i=(ll)from; i<(ll)to; i++)
#define all(vec) vec.begin(), vec.end()
#define rep(i,N) repr(i,0,N)
#define per(i,N) for (int i=(int)N-1; i>=0; i--)

const ll MOD = pow(10,9)+7;
const ll LLINF = pow(2,61)-1;
const int INF = pow(2,30)-1;

vector<ll> fac;
void c_fac(int x=pow(10,6)+10) { fac.resize(x,true); rep(i,x) fac[i] = i ? (fac[i-1]*i)%MOD : 1; }
ll modpow(ll x, ll p) { ll result = 1, now = 1, pm = x; while (now<=p) { if (p&now) { result = result * pm % MOD; } now*=2; pm = pm*pm % MOD; } return result; }
ll inv(ll a, ll m=MOD) { ll b = m, x = 1, y = 0; while (b!=0) { int d = a/b; a -= b*d; swap(a,b); x -= y*d; swap(x,y); } return (x+m)%m; }
ll nck(ll n, ll k) { return fac[n]*inv(fac[k]*fac[n-k]%MOD)%MOD; }
ll gcd(ll a, ll b) { if (a<b) swap(a,b); return b==0 ? a : gcd(b, a%b); }
ll lcm(ll a, ll b) { return a/gcd(a,b)*b; }


int main() {
  ll N; cin >> N;
  vector<ll> yaku; yaku.push_back(N);
  repr(i,1,N) if ((N*N)%i==0) { yaku.push_back(i); yaku.push_back((N*N)/i); }
  sort(all(yaku));

  ll s = yaku.size();
  ll c1 = 0, c2 = 0, c3 = 0;
  rep(i,s) rep(j,s) {
    if ((N*N)%(yaku[i]*yaku[j])) continue;
    ll r = (yaku[i]+yaku[j])*(yaku[i]+yaku[j])+4*N*N/(yaku[i]*yaku[j]), sqr = sqrt(r);
    if (r<0||sqr*sqr!=r||(sqr-(yaku[i]+yaku[j]))%2) continue;
    ll k = (sqr-(yaku[i]+yaku[j])) / 2;
    if (yaku[i]==yaku[j]&&yaku[j]==k) c3++;
    else if (yaku[i]==yaku[j]||yaku[j]==k||k==yaku[i]) c2++;
    else c1++;
    // cout << yaku[i] << " " << yaku[j] << " " << k << endl;
  }
  ll result = c1/6 + c2/3 + c3;
  cout << result << endl;
  return 0;
}