test.cpp

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

int main() {
    int N;
    cin >> N;

    vector<int> a(N), b(N);
    for (int i = 0; i < N; ++i) cin >> a[i];
    for (int i = 0; i < N; ++i) cin >> b[i];

    // Step 1: Calculate the valid ranges and store their midpoints
    vector<int> possible_values;
    for (int i = 0; i < N; ++i) {
        possible_values.push_back(a[i]);
        possible_values.push_back(a[i] + b[i]);
    }

    // Step 2: Sort to find the median
    sort(possible_values.begin(), possible_values.end());
    int median = possible_values[possible_values.size() / 2];

    // Step 3: Clamp each value to be as close as possible to the median
    vector<int> x(N);
    for (int i = 0; i < N; ++i) {
        x[i] = max(a[i], min(a[i] + b[i], median));
    }

    // Step 4: Calculate the minimized value of S
    long long sum_x = 0, sum_x2 = 0;
    for (int i = 0; i < N; ++i) {
        sum_x += x[i];
        sum_x2 += 1LL * x[i] * x[i];
    }

    long long result = 2LL * N * sum_x2 - 2LL * sum_x * sum_x;
    cout << result << endl;

    return 0;
}