#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
#define ALL(v) v.begin(),v.end()
#define dbg(x) cerr << #x << ": " << (x) << endl;

mt19937 rnd;
int n;
vector<int> h,p;

void input() {
    cin >> n;
    h.resize(n);
    p.resize(n);
    for (int i = 0; i < n; ++i) cin >> h[i];
    for (int i = 0; i < n; ++i) cin >> p[i];
}

void gen() {
    n = 5;
    h.resize(n);
    p.resize(n);
    for (int i = 0; i < n; ++i) h[i] = rnd() % 10;
    // sort(ALL(h));
    for (int i = 0; i < n; ++i) p[i] = rnd() % 10 + h[i];
}

int naive() {
    int cnt = 0;
    for (int i = 0; i < n; ++i) if (p[i] < h[i]) return -1;
    while (true) {
        int idx = 1e9;
        for (int i = 0; i < n; ++i) if (p[i] > h[i]) {
            if (idx < n) {
                if (p[idx] - h[idx] < p[i] - h[i]) {
                    idx = i;
                }
            }
            else {
                idx = i;
            }
        }
        if (idx == 1e9) break;
        int mi = p[idx];
        for (int i = 0; i < n; ++i) if (p[i] >= mi) {
            if (p[i] - 1 < h[i]) {
                return -1;
            }
            p[i] -= 1;
        }
        ++cnt;
    }
    return cnt;
}

int solve() {

    vector<int> ord(n);
    iota(ALL(ord),0);
    sort(ALL(ord), [&](int i, int j) {
        return p[i] < p[j];
    });
    
    bool ok = true;
    for (int i = 0; i+1 < n; ++i) {
        int x = ord[i];
        int y = ord[i+1];
        if (p[x] == p[y]) {
            if (h[x] != h[y]) {
                ok = false;
                break;
            }
        }
        else {
            if (h[x] > h[y]) {
                ok = false;
                break;
            }
        }
    }
    if (ok) {
        for (int i = 0; i < n; ++i) if (p[i] < h[i]) {
            ok = false;
            break;
        }
    }
    int ans = -1;
    if (ok) {
        ans = p[ord.back()] - h[ord.back()];
    }

    return ans;
}

int main() {
    int t;
    cin >> t;
    while (t--) {
        input();
        cout << solve() << '\n';
    }

    // while (true) {
    //     gen();
    //     auto ch = h, cp = p;
    //     int x = solve();
    //     int y = naive();
    //     dbg(x)
    //     if (x != y) {
    //         for (int i = 0; i < n; ++i) {
    //             cerr << ch[i] << " \n"[i==n-1];
    //         }
    //         for (int i = 0; i < n; ++i) {
    //             cerr << cp[i] << " \n"[i==n-1];
    //         }
    //         dbg(x)
    //         dbg(y)
    //         break;
    //     }
    // }
}