vector<int> edges[200001];

bool dfs(int n, int des){

if(n == des) return true;

for(unsigned int i=0; i<edges[n].size(); i++){

if(edges[n][i] == n+1){

return dfs(n+1, des);

}

}

return false;

}

bool solution1(int N, vector<int> &A, vector<int> &B){

for(unsigned int i = 0; i < A.size(); i++){

edges[A[i]].push_back(B[i]);

edges[B[i]].push_back(A[i]);

}

return dfs(1, N);

}

string solution2(string riddle){

string answer = "";

for(int i=0; i<riddle.length(); i++){

bool check[26];

for(int j=0; j<26; j++) check[j] = true;

if(riddle[i] != '?'){

answer += riddle[i];

continue;

}

if(i>0){

check[answer[i-1]-'a'] = false;

}

if(i<riddle.length()-1 && riddle[i+1] != '?'){

check[riddle[i+1]-'a'] = false;

}

for(int j=0; j<26; j++){

if(check[j]){

answer += 'a'+j;

break;

}

}

}

return answer;

}

int solution4(vector<int> numbers){

int count[31];

for(int i=0; i<=30; i++) count[i] = 0;

for(unsigned i = 0; i < numbers.size(); i++){

int now = numbers[i];

int k = 0;

while(now > 0){

if(now%2 == 1){

count[k]++;

}

now = now / 2;

k++;

}

}

int ans = 0;

for(int i=0; i<=30; i++){

ans = max(ans, count[i])

}

return ans;

}

vector<int> digits_sum[51];

int get_sum_of_digits(int n){

if(n<10) return n;

return get_sum_of_digits(n / 10) + n%10;

}

int solution5(vector<int> numbers){

for(unsigned int i=0; i<numbers.size(); i++){

int idx = get_sum_of_digits(numbers[i]);

digits_sum[idx].push_back(numbers[i]);

}

int ans = -1;

for(int i=0; i<=50; i++){

if(digits_sum[i].size() > 1){

sort(digits_sum[i].begin(), digits_sum[i].end());

unsigned int length = digits_sum[i].size();

ans = max(ans, digits_sum[i][length-1] + digits_sum[i][length-2]);

}

}

}