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<int> newconn;
    int count = 0;
    for (int i = 0; i < n - 2; i++) {
        if (conn.at(i).size() == 2) {
            count++;
            newconn.push_back(conn.at(i).front());
        }
    }
    std::cout << count - 1 << std::endl;
    for (int i = 0; i < count - 1; i++) {
        std::cout << newconn.at(i) << ' ' << newconn.at((i+1)%count) << std::endl;
    }
}

Test 1

Verdict: WRONG ANSWER

Test 2

Verdict: ACCEPTED

Test 3

Verdict: WRONG ANSWER

Test 4

Verdict: WRONG ANSWER

Test 5

Verdict: WRONG ANSWER

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: WRONG ANSWER

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: WRONG ANSWER

Test 19

Verdict: WRONG ANSWER

Test 20

Verdict: WRONG ANSWER

Test 21

Verdict: WRONG ANSWER