//Question: What is the issue in the following code and how to fix it:

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int INF = 1e9;

/***
 * Given boxes of balls of certain colors,
 * determine the minimum number of operations that guarantee
 * to have two balls of the same color.
 * In one operation, you can choose a box and get a random ball
 * from the remaining balls in the chosen box.
 * @param n the number of boxes.
 * @param m the number of colors.
 * @param boxes the colors of the balls in each box.
 * @return the minimum number of operations that guarantee
 * to have two balls of the same color.
 */
int guaranteeTheWin(int n, int m, const vector<vector<int>>& boxes){
    int ans = INT_MAX;
    set<int> s[n];
    vector<int> min1(m+1, INF), min2(m+1, INF);
    for (int i = 0; i < n; ++i) {
        for(int c : boxes[i])
            s[i].insert(c);

        int distinct = s[i].size();
        for(int c : s[i]){
            if(distinct < min1[c])
                min2[c] = min1[c], min1[c] = distinct;
            else if(distinct < min2[c])
                min2[c] = distinct;
        }

        // get 2 balls of this box
        if(boxes[i].size() > distinct)
            ans = min(ans, distinct + 1);
    }

    // choose a ball from box i, then either continue choosing from i
    // or guarantee to pick the last picked color from another box.
    for (int i = 0; i < n; ++i) {
        priority_queue<int> pq;
        int distinct = s[i].size();
        for(int c : s[i]){
            if(distinct == min1[c])
                pq.push(min2[c]);
            else
                pq.push(min1[c]);
        }

        int ops = 1;
        while (!pq.empty()){
            ans = min(ans, ops + pq.top());
            pq.pop();
            ops++;
        }
    }

    return ans;
}

int main() {
    int n, m;
    cin >> n;
    vector<vector<int>> boxes(n);
    for (int i = 0; i < n; ++i) {
        int sz;
        cin >> sz;
        boxes[i].resize(sz);
        for(int &e : boxes[i]){
            cin >> e;
            m = max(m, e);
        }
    }
    cout << guaranteeTheWin(n,m,boxes);
    return 0;
}