#include <bits/stdc++.h>
using namespace std;
 
#define ms(s, n) memset(s, n, sizeof(s))
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define FORd(i, a, b) for (int i = (a) - 1; i >= (b); i--)
#define FORall(it, a) for (__typeof((a).begin()) it = (a).begin(); it != (a).end(); it++)
#define sz(a) int((a).size())
#define present(t, x) (t.find(x) != t.end())
#define all(a) (a).begin(), (a).end()
#define uni(a) (a).erase(unique(all(a)), (a).end())
#define pb push_back
#define pf push_front
#define mp make_pair
#define fi first
#define se second
#define prec(n) fixed<<setprecision(n)
#define bit(n, i) (((n) >> (i)) & 1)
#define bitcount(n) __builtin_popcountll(n)
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pi;
typedef vector<int> vi;
typedef vector<pi> vii;
const int MOD = (int) 1e9 + 7;
const int MOD2 = 1007681537;
const int INF = (int) 1e9;
const ll LINF = (ll) 1e18;
const ld PI = acos((ld) -1);
const ld EPS = 1e-9;
inline ll gcd(ll a, ll b) {ll r; while (b) {r = a % b; a = b; b = r;} return a;}
inline ll lcm(ll a, ll b) {return a / gcd(a, b) * b;}
inline ll fpow(ll n, ll k, int p = MOD) {ll r = 1; for (; k; k >>= 1) {if (k & 1) r = r * n % p; n = n * n % p;} return r;}
template<class T> inline int chkmin(T& a, const T& val) {return val < a ? a = val, 1 : 0;}
template<class T> inline int chkmax(T& a, const T& val) {return a < val ? a = val, 1 : 0;}
inline ll isqrt(ll k) {ll r = sqrt(k) + 1; while (r * r > k) r--; return r;}
inline ll icbrt(ll k) {ll r = cbrt(k) + 1; while (r * r * r > k) r--; return r;}
inline void addmod(int& a, int val, int p = MOD) {if ((a = (a + val)) >= p) a -= p;}
inline void submod(int& a, int val, int p = MOD) {if ((a = (a - val)) < 0) a += p;}
inline int mult(int a, int b, int p = MOD) {return (ll) a * b % p;}
inline int inv(int a, int p = MOD) {return fpow(a, p - 2, p);}
inline int sign(ld x) {return x < -EPS ? -1 : x > +EPS;}
inline int sign(ld x, ld y) {return sign(x - y);}
#define db(x) cerr << #x << " = " << (x) << " ";
#define endln cerr << "\n";
 
#define double __float128
struct PT {
    int x, y;
    PT(int x = 0, int y = 0) : x(x), y(y) {}
    PT operator - (const PT& rhs) {
        return PT(x - rhs.x, y - rhs.y);
    }
};
 
long long cross(PT a, PT b) {
    return (long long) a.x * b.y - (long long) a.y * b.x;
}
 
double dist(PT a, PT b) {
    return sqrt((ld) (a.x - b.x) * (a.x - b.x) + (ld) (a.y - b.y) * (a.y - b.y));
}
 
const int maxn = 1e5 + 5;
int n;
PT p[maxn];
int w[maxn];
double dp[maxn];
 
//dp[i] = max(dp[j] + dist(i, j) - mi * w[i])
void divide(int L, int R, int optL, int optR, double mi) {
    if (L > R) return;
    int M = L + R >> 1;
    pair<double, int> best = mp(-1e100, -1);
    FOR(i, optL, min(M, optR + 1)) {
        chkmax(best, mp(dp[i] + dist(p[i], p[M]), i));
    }
    dp[M] = best.fi - mi * w[M];
    divide(L, M - 1, optL, best.se, mi);
    divide(M + 1, R, best.se, optR, mi);
}
 
void solve() {
    int test; cin >> test;
    int nsum = 0;
    while (test--) {
        cin >> n;
        assert(3 <= n && n <= 1e5);
        nsum += n;
        FOR(i, 0, n) {
            cin >> p[i].x >> p[i].y;
            assert(0 <= p[i].x && p[i].x <= 1e9);
            assert(0 <= p[i].y && p[i].y <= 1e9);
        }
        FOR(i, 0, n) {
            cin >> w[i];
            assert(1 <= w[i] && w[i] <= 1e9);
        }
        __int128 area = 0;
        FOR(i, 0, n) {
            int j = (i + 1) % n;
            area += cross(p[i], p[j]);
        }
        if (area < 0) {
            reverse(p + 1, p + n);
            reverse(w + 1, w + n);
        }
        FOR(i, 0, n) {
            int j = (i + 1) % n;
            int k = (i + 2) % n;
            assert(cross(p[k] - p[j], p[i] - p[j]) > 0);
        }
        double lo = 0, hi = 1e10;
        FOR(it, 0, 100) {
            double mi = (lo + hi) / 2;
            divide(1, n - 1, 0, n - 1, mi);
            double mx = -1e100;
            FOR(i, 1, n) {
                chkmax(mx, dp[i] + dist(p[i], p[0]) - mi * w[0]);
            }
            if (mx >= 0) {
                lo = mi;
            }
            else {
                hi = mi;
            }
        }
        cout << prec(9) << (ld) ((lo + hi) / 2) << "\n";
    }
    assert(1 <= n && n <= 2e5);
}
 
int main() {
    int JUDGE_ONLINE = 1;
    if (fopen("in.txt", "r")) {
        JUDGE_ONLINE = 0;
        assert(freopen("in.txt", "r", stdin));
        assert(freopen("out.txt", "w", stdout));
    }
    else {
        ios_base::sync_with_stdio(0), cin.tie(0);
    }
    solve();
    if (!JUDGE_ONLINE) {
        //cout << "\nTime elapsed: " << 1000 * clock() / CLOCKS_PER_SEC << "ms\n";
    }
    return 0;
}