Tanzir vai dinic

/*
The Great Template of Salazar Slytherin
*/
#include <bits/stdc++.h>

using namespace std;

#define rep(i,n) for(i=0; i<n; i++)
#define repl(i,n) for(i=1; i<=n; i++)

#define sz(x) (int) x.size()
#define pb  push_back
#define all(x) x.begin(),x.end()
#define uu first
#define vv second
#define mem(x, y) memset(x, y, sizeof(x));

#define sdi(x) scanf("%d", &x)
#define sdii(x, y) scanf("%d %d", &x, &y)
#define sdiii(x, y, z) scanf("%d %d %d", &x, &y, &z)
#define sdl(x) scanf("%lld", &x)
#define sdll(x, y) scanf("%lld %lld", &x, &y)
#define sdlll(x, y, z) scanf("%lld %lld %lld", &x, &y, &z)
#define sds(x) scanf("%s", x)
#define pfi(x) printf("%d\n", x)
#define pfii(x, y) printf("%d %d\n", x, y)
#define pfiii(x, y, z) printf("%d %d %d\n", x, y, z)
#define pfl(x) printf("%lld\n", x)
#define pfll(x, y) printf("%lld %lld\n", x, y)
#define pflll(x, y, z) printf("%lld %lld %lld\n", x, y, z)

#define eps 1e-13
#define OK printf("ok\n")
#define DB(x) cout << #x << " = " << x << endl;

/// Tanzir
#define FRE(i,a,b)  for(i = a; i <= b; i++)
#define FRL(i,a,b)  for(i = a; i < b; i++)
#define un(x)       x.erase(unique(all(x)), x.end())
#define sf(n)       scanf("%d", &n)
#define sff(a,b)    scanf("%d %d", &a, &b)
#define sfff(a,b,c) scanf("%d %d %d", &a, &b, &c)
#define sl(n)       scanf("%lld", &n)
#define sll(a,b)    scanf("%lld %lld", &a, &b)
#define slll(a,b,c) scanf("%lld %lld %lld", &a, &b, &c)
#define D(x)        cout<<#x " = "<<(x)<<endl
#define DBG         printf("Hi\n")
#define PI          acos(-1.00)
#define xx          first
#define yy          second

typedef double db;
typedef long long LL;
typedef unsigned long long ULL;
typedef pair <int, int> pii;
typedef pair <long long , long long > pll;

inline int setBit(int N, int pos) { return N=N | (1<<pos); }
inline int resetBit(int N, int pos) { return N= N & ~(1<<pos); }
inline bool checkBit(int N, int pos) { return (bool)(N & (1<<pos)); }

//int kx[] = {+2, +1, -1, -2, -2, -1, +1, +2};
//int ky[] = {+1, +2, +2, +1, -1, -2, -2, -1}; //Knight Direction
//int fx[] = {+0, +0, +1, -1, -1, +1, -1, +1};
//int fy[] = {-1, +1, +0, +0, +1, +1, -1, -1}; //Four & Eight Direction

/// Zobayer vai's code

const int MAXN = 105, MAXE = 500+505; // MAXE = twice the number of edges
int src, snk, nNode, nEdge;
LL Q[MAXN], fin[MAXN], pro[MAXN], dist[MAXN];
LL flow[MAXE], cap[MAXE], nxt[MAXE], to[MAXE];
const LL inf = 1e9;
inline void init(int _src, int _snk, int _n)
{
    src = _src, snk = _snk, nNode = _n, nEdge = 0;
    mem(fin, -1);
}

inline void add(int u, int v, LL _cap)
{
//    D(_cap);
    to[nEdge] = v, cap[nEdge] = _cap, flow[nEdge] = 0, nxt[nEdge] = fin[u], fin[u] = nEdge++;
    to[nEdge] = u, cap[nEdge] = 0, flow[nEdge] = 0, nxt[nEdge] = fin[v], fin[v] = nEdge++; // for directed cap[nEdge]=0 here
}

bool bfs()
{
    int st, en, i, u, v;
    mem(dist, -1);
    dist[src] = st = en = 0;
    Q[en++] = src;
    while(st < en)
    {
        u = Q[st++];
        for(i=fin[u]; i>=0; i=nxt[i])
        {
            v = to[i];
            if(flow[i] < cap[i] && dist[v]==-1)
            {
                dist[v] = dist[u]+1;
                Q[en++] = v;
            }
        }
    }
    return dist[snk]!=-1;
}

LL dfs(LL u, LL fl)
{
    if(u==snk) return fl;
    for(LL &e=pro[u], v, df; e>=0; e=nxt[e])
    {
        v = to[e];
        if(flow[e] < cap[e] && dist[v]==dist[u]+1)
        {
            df = dfs(v, min(cap[e]-flow[e], fl));
            if(df>0)
            {
                flow[e] += df;
                flow[e^1] -= df;
                return df;
            }
        }
    }
    return 0;
}

LL dinitz()   // 1-based indexing
{
    LL ret = 0;
    LL df;
    while(bfs())
    {
        for(int i=1; i<=nNode; i++) pro[i] = fin[i];
        while(true)
        {
            df = dfs(src, inf);
            if(df) ret += df;
            else break;
        }
    }
    return ret;
}
struct edge{
    int u, v, c;
};
vector<edge> E;
int n, m, x;
bool ok(db mid)
{
//    D(mid);
    int src = n+1;
    init(src,n,n+1);
    add(src,1,x);
    for(int i = 0; i<E.size(); i++)
        add(E[i].u,E[i].v,(E[i].c/mid)+eps);
    if(dinitz() == x)
        return true;
    return false;
}
int main()
{
//    freopen("in.txt","r",stdin);
//    freopen("out.txt","w",stdout);
    int i, j, cs, t, u, v,c;
    sfff(n,m,x);
    FRE(i,1,m)
    {
        sfff(u,v,c);
        E.pb({u,v,c});
    }
    db lo = eps, hi = 2e6;
//    D(ok(1.0/x));return 0;

//    if(n == 50)
//        D(ok(4160084.5279072807));
    for(int i = 1; i<=400; i++)
    {
        db mid = (lo+hi)/2;
        if(ok(mid))
            lo = mid;
        else
            hi = mid;
    }
    printf("%.10f\n",x*lo);

    return 0;
}