Description


 In ICPCCamp, there are  n cities and  m unidirectional roads between cities. The  i-th road goes from the a i-th city to the b i-th city. For each pair of cities  u and  v, there is at most one road from  u to  v.



As traffic in ICPCCamp is becoming heavier, toll of the roads also varies. At time  t, one should pay (c i⋅t+d i) dollars to travel along the  i-th road.



Bobo living in the 1-st city would like to go to the n-th city. He wants to know the average money he must spend at least if he starts from city 1 at  t∈[0,T]. Note that since Bobo's car is super-fast, traveling on the roads costs him  no time.



Formally, if  f(t) is the minimum money he should pay from city 1 to city  n at time  t, Bobo would like to find







Input


4).


i,b i,c i,d i (1≤a i,b i≤n,a i≠b i,0≤c i,d i≤10 3).


It is guaranteed that Bobo is able to drive from city 1 to city n.


Output


-6.


Sample Input

3 3 2
1 2 1 0
2 3 1 0
1 3 1 1
3 3 2
1 2 1 0
2 3 1 0
1 3 0 5

Sample Output

#include<set>
#include<map>
#include<ctime>
#include<cmath>
#include<stack>
#include<queue>
#include<bitset>
#include<cstdio>
#include<string>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<functional>
#define rep(i,j,k) for (int i = j; i <= k; i++)
#define per(i,j,k) for (int i = j; i >= k; i--)
#define loop(i,j,k) for (int i = j;i != -1; i = k[i])
#define lson x << 1, l, mid
#define rson x << 1 | 1, mid + 1, r
#define ff first
#define ss second
#define mp(i,j) make_pair(i,j)
#define pb push_back
#define pii pair<int,int>
#define in(x) scanf("%d", &x);
using namespace std;
typedef long long LL;
const int low(int x) { return x&-x; }
const double eps = 1e-8;
const int INF = 0x7FFFFFFF;
const int mod = 1e9 + 7;
const int N = 15;
int n, m, t, x, y;
int c[N][N], d[N][N];
double dis[N];
int u[N], v[N], vis[N];

pii check(double t)
{
  rep(i, 1, n) dis[i] = -1, u[i] = v[i] = vis[i] = 0;
  dis[1] = 0;
  while (true)
  {
    x = 0;
    rep(i, 1, n)
    {
      if (dis[i] < 0 || vis[i]) continue;
      if (!x || dis[i] < dis[x]) x = i;
    }
    if (!x) break; vis[x] = 1;
    rep(i, 1, n)
    {
      if (c[x][i] == -1) continue;
      if (dis[i]<0 || dis[i] - eps > dis[x] + t*c[x][i] + d[x][i])
      {
        dis[i] = dis[x] + t*c[x][i] + d[x][i];
        u[i] = u[x] + c[x][i];
        v[i] = v[x] + d[x][i];
      }
      else if (fabs(dis[x] + t*c[x][i] + d[x][i] - dis[i]) < eps)
      {
        if (u[i] > u[x] + c[x][i])
        {
          u[i] = u[x] + c[x][i];
          v[i] = v[x] + d[x][i];
        }
      }
    }
  }
  return mp(u[n], v[n]);
}

int main()
{
  while (scanf("%d%d%d", &n, &m, &t) != EOF)
  {
    memset(c, -1, sizeof(c));
    while (m--)
    {
      scanf("%d%d", &x, &y);
      scanf("%d%d", &c[x][y], &d[x][y]);
    }
    double l = 0, r = t, ans = 0;
    pii bef = check(l);
    while (l + eps < r)
    {
      double q = l, h = r;
      pii now;
      while (q + eps < h)
      {
        now = check((q + h) / 2);
        if (now.ff == bef.ff) q = (q + h) / 2;
        else h = (q + h) / 2;
      }
      ans += (h - l) * ((h + l) / 2 * bef.ff + bef.ss);
      bef = check(l = h);
    }
    printf("%.8lf\n", ans / t);
  }
  return 0;
}
#include<set>
#include<map>
#include<ctime>
#include<cmath>
#include<stack>
#include<queue>
#include<bitset>
#include<cstdio>
#include<string>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<functional>
#define rep(i,j,k) for (int i = j; i <= k; i++)
#define per(i,j,k) for (int i = j; i >= k; i--)
#define loop(i,j,k) for (int i = j;i != -1; i = k[i])
#define lson x << 1, l, mid
#define rson x << 1 | 1, mid + 1, r
#define ff first
#define ss second
#define mp(i,j) make_pair(i,j)
#define pb push_back
#define pii pair<int,int>
#define in(x) scanf("%d", &x);
using namespace std;
typedef long long LL;
const int low(int x) { return x&-x; }
const double eps = 1e-8;
const int INF = 0x7FFFFFFF;
const int mod = 1e9 + 7;
const int N = 15;
int n, m, t, x, y;
int c[N][N], d[N][N];
double dis[N];
int vis[N];

double get(double t)
{
  rep(i, 1, n) dis[i] = -1, vis[i] = 0;
  dis[1] = 0;
  while (true)
  {
    x = 0;
    rep(i, 1, n)
    {
      if (dis[i] < 0 || vis[i]) continue;
      if (!x || dis[i] < dis[x]) x = i;
    }
    if (!x) break; vis[x] = 1;
    rep(i, 1, n)
    {
      if (c[x][i] == -1) continue;
      if (dis[i] > eps && dis[i] + eps < dis[x] + t*c[x][i] + d[x][i]) continue;
      dis[i] = dis[x] + t * c[x][i] + d[x][i];
    }
  }
  return dis[n];
}

double simpson(double l, double r)
{
  return (r - l) / 6 * (get(l) + 4 * get((l + r) / 2) + get(r));
}

double solve(double l, double r)
{
  double mid = (l + r) / 2, now = simpson(l, r);
  if (fabs(simpson(l, mid) + simpson(mid, r) - now) < eps) return now;
  return solve(l, mid) + solve(mid, r);
}

int main()
{
  while (scanf("%d%d%d", &n, &m, &t) != EOF)
  {
    memset(c, -1, sizeof(c));
    while (m--)
    {
      scanf("%d%d", &x, &y);
      scanf("%d%d", &c[x][y], &d[x][y]);
    }
    printf("%.8lf\n", solve(0, t) / t);
  }
  return 0;
}