#include <algorithm>

#include  <iterator>

#include  <iostream>

#include   <cstring>

#include   <cstdlib>

#include   <iomanip>

#include    <bitset>

#include    <cctype>

#include    <cstdio>

#include    <string>

#include    <vector>

#include     <stack>

#include     <cmath>

#include     <queue>

#include      <list>

#include       <map>

#include       <set>

#include   <cassert>

using namespace std;

#define lson (l , mid , rt << 1)

#define rson (mid + 1 , r , rt << 1 | 1)

#define debug(x) cerr << #x << " = " << x << "\n";

#define pb push_back

#define pq priority_queue

typedef long long ll;

typedef unsigned long long ull;

//typedef __int128 bll;

typedef pair<ll ,ll > pll;

typedef pair<int ,int > pii;

typedef pair<int,pii> p3;

//priority_queue<int> q;//这是一个大根堆q

//priority_queue<int,vector<int>,greater<int> >q;//这是一个小根堆q

#define fi first

#define se second

//#define endl '\n'

//#define R register

#define OKC ios::sync_with_stdio(false);cin.tie(0)

#define FT(A,B,C) for(int A=B;A <= C;++A)  //用来压行

#define REP(i , j , k)  for(int i = j ; i <  k ; ++i)

#define max3(a,b,c) max(max(a,b), c);

#define min3(a,b,c) min(min(a,b), c);

//priority_queue<int ,vector<int>, greater<int> >que;

const ll mos = 0x7FFFFFFF;  //

const ll nmos = 0x80000000;  //-2147483648

const int inf = 0x3f3f3f3f;

const ll inff = 0x3f3f3f3f3f3f3f3f; //

const int mod = 1e9+;

const double esp = 1e-;

const double PI=acos(-1.0);

const double PHI=0.61803399;    //黄金分割点

const double tPHI=0.38196601;

template<typename T>

inline T read(T&x){

    x=;int f=;char ch=getchar();

    while (ch<''||ch>'') f|=(ch=='-'),ch=getchar();

    while (ch>=''&&ch<='') x=x*+ch-'',ch=getchar();

    return x=f?-x:x;

}

/*-----------------------showtime----------------------*/

            const int maxn = ;

            struct node{

                ll x1,y1,x2,y2;

            }a[maxn];

            ll ans = ;

            map<pii, int> mp;

            void cal(int i,int j){

                    ll x1 = a[i].x1,y1 = a[i].y1,x2 = a[i].x2,y2 = a[i].y2;

                    ll x3 = a[j].x1,y3 = a[j].y1,x4 = a[j].x2,y4 = a[j].y2;

                    ll a = (y1-y2) * (x4-x3) - (x2-x1)*(y3-y4);

                    ll t = (x2*y1 - x1*y2)*(x4-x3) - (x2-x1)*(x4*y3 - x3*y4);

                    ll p = (y1-y2) * (x4*y3-x3*y4) - (x2*y1-x1*y2)*(y3-y4);

                    if(a == )return;

                    if(t % a || p % a) return;

                    t = t/a; p = p/a;

                    if(x1 > x2) swap (x1,x2);   if(t < x1 || t > x2) return;

                    if(x3 > x4) swap (x3,x4);   if(t < x3 || t > x4) return;

                    if(y1 > y2) swap(y1,y2);    if(p < y1 || p > y2) return;

                    if(y3 > y4) swap(y3,y4);    if(p < y3 || p > y4) return;

                    mp[pii(t,p)] ++;

            }

int main(){

            int n;  scanf("%d", &n);

            for(int i=; i<=n; i++){

                ll x1,y1,x2,y2;

                scanf("%lld%lld%lld%lld", &x1, &y1, &x2, & y2);

                a[i] = (node){x1,y1,x2,y2};

                ll d1 = abs(x1 - x2);

                ll d2 = abs(y1 - y2);

                ans += __gcd(d1, d2) + ;

            }

            for(int i=; i<=n; i++){

                for(int j=; j<=n; j++){

                    if(i == j) continue;

                    cal(i,j);

                }

            }

            for(auto p : mp){

                ans -= (int)sqrt(p.se);

            }

            printf("%lld\n", ans);

            return ;

}