Fragile network

#include <iostream>
#include <vector>
#include <algorithm>


int main() {
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(NULL);
    int n;
    std::cin >> n;
    std::vector<std::vector<int>> conn;
    for (int i = 1; i <= n; i++) {
        conn.push_back({i});
    }
    for (int i = 0; i < n - 1; i++) {
        int a, b;
        std::cin >> a >> b;
        conn.at(a - 1).push_back(b);
        conn.at(b - 1).push_back(a);
    }
    std::sort(conn.begin(), conn.end(), [](const std::vector<int>& a, 
            const std::vector<int>& b) { return a.size() <= b.size(); });
    std::vector<std::pair<int, int>> newconn;
    int count = 0;
    for (int i = 0; i < n - 2; i++) {
        if (conn.at(i).size() == 2) {
            int curr = i + 1;
            if (std::find(conn.at(i).begin() + 1, conn.at(i).end(), conn.at(curr).front()) != conn.at(i).end()) {
                curr++;
                if (std::find(conn.at(i).begin() + 1, conn.at(i).end(),
                 conn.at(curr).front()) != conn.at(i).end()) curr++;
            }
            newconn.push_back({conn.at(i).front(), conn.at(curr).front()});
            count++;
            conn.at(curr).push_back(i + 1);
            conn.at(i).push_back(curr + 1);
        }
    }
    std::cout << count << std::endl;
    for (auto& pa : newconn) {
        std::cout << pa.first << ' ' << pa.second << std::endl;
    }
}

Test 1

Verdict: WRONG ANSWER

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: RUNTIME ERROR

Test 7

Verdict: RUNTIME ERROR

Test 8

Verdict: RUNTIME ERROR

Test 9

Verdict: RUNTIME ERROR

Test 10

Verdict: RUNTIME ERROR

Test 11

Verdict: ACCEPTED

Test 12

Verdict: WRONG ANSWER

Test 13

Verdict: WRONG ANSWER

Test 14

Verdict: RUNTIME ERROR

Test 15

Verdict: WRONG ANSWER

Test 16

Verdict: WRONG ANSWER

Test 17

Verdict: WRONG ANSWER

Test 18

Verdict: ACCEPTED

Test 19

Verdict: ACCEPTED

Test 20

Verdict: ACCEPTED

Test 21

Verdict: ACCEPTED