#include <cstdio>
#include <vector>
#include <set>
#include <iostream>
#include <iomanip>
#include <algorithm>
using namespace std;

float mean(vector<float> data){
    auto length = data.size();
    float res{0};
    for(int i = 0; i<length; i++){
        res+=data[i];
    }
    return res / length;
}

float covariance(vector<float>x,vector<float>y){
    int n = x.size();
    float mx{mean(x)}, my{mean(y)};
    float res{0};
    for(int i=0;i<n;i++){
        res+=(x[i]-mx)*(y[i]-my);
    }
    return res / n;
}

float sdev(vector<float>d){
    int n = d.size();
    float md{mean(d)};
    float res{0};
    for(int i=0;i<n;i++){
        res+=pow((d[i]-md),2);
    }
    return sqrt(res/n);
}

float pearson(vector<float>x, vector<float>y){
    return covariance(x, y) / (sdev(x)*sdev(y));
}

int set_index(set<float> s, float val)
{
    int i = 1;
 
    for (auto u : s) {
        if (u == val){
           return i; 
        }   
        i++;
    }
    return -1;
}

vector<float>rank_vector(vector<float>d){
    set<float>s;
    for(auto el : d){
        s.insert(el);
    }
    int n = d.size();
    vector<float>res(n);
    for(int i = 0; i<n; i++){
        res[i]=(float)set_index(s, d[i]);
    }
    return res;
}


int main() {
    int n{};
    cin >> n;
    vector<float> x(n), y(n);
    for(int i =0; i < n; i++){
        cin >> x[i];
    }
    for(int i =0; i < n; i++){
        cin >> y[i];
    }
    cout << fixed << setprecision(3)
         << pearson(rank_vector(x), rank_vector(y)) << endl;  
    return 0;
}

#python
n=int(input())
X=list(map(float, input().split()))
Y=list(map(float, input().split()))
res=[(sorted(X).index(X[i])-sorted(Y).index(Y[i]))**2 for i in range(n)]
srcc=1-(6*sum(res)/(n*(n**2-1)))
print(round(srcc, 3))

#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
#include <iomanip>
using namespace std;

int getIndexOf(double a, vector<double> y)
{
    int count=1;
    for (int j=0; j<y.size(); ++j)
    {
        if (a==y[j])
            break;
        else
            count++;
    }
    return count;
}

vector<int> getRank(vector<double> x)
{
    vector<int> xVar(x.size());
    vector<double> x_sorted(x.size());
    partial_sort_copy(begin(x), end(x), begin(x_sorted), end(x_sorted));
    for(int i=0; i<x.size(); ++i)
    {
        int index=getIndexOf(x[i], x_sorted);
        xVar[i]=index;
    }
    return xVar;
}

int main() {
    /* Enter your code here. Read input from STDIN. Print output to STDOUT */   
    int n;
    cin>>n;
    
    vector<double> x,y;
    double num=0;
    for(int i=0; i<n; ++i){
        cin>>num;
        x.push_back(num);
    }
    
    for(int i=0; i<n; ++i){
        cin>>num;
        y.push_back(num);
    }
    vector<int> rankX=getRank(x);
    vector<int> rankY=getRank(y);
    
    double r=0;
    for (int i=0; i<n; ++i)
    {
        r+=pow((rankX[i]-rankY[i]),2.);
    }
    cout<<fixed<<setprecision(3);
    cout<<1-6*r/(n*n*n-n);
    return 0;
}

n = int(input())
X = list(map(float, input().split()))
Y = list(map(float, input().split()))

X_sort = sorted(X)
Y_sort = sorted(Y)

rank_X = []
rank_Y = []

for i in range(n):
    for j in range(n):
        if X[i] == X_sort[j]:
            rank_X.append(j+1)
        if Y[i] == Y_sort[j]:
            rank_Y.append(j+1)

d = 0
for i in range(n):
    d += pow((rank_X[i] - rank_Y[i]), 2)
    
Spearman_rank_coef = 1 - 6 * d / (n * (n * n - 1))
print(round(Spearman_rank_coef, 3))

n = int(input())
a = list(map(float, input().split()))
b = list(map(float, input().split()))
ranks = lambda x : [sorted(x).index(i)+1 for i in x]
spear = lambda n,a,b : 1-6*sum([(i[0]-i[1])**2 for i in list(zip(ranks(a),ranks(b)))]) / (n*(n**2-1))
print(round(spear(n,a,b),3))