Topological Sorting - Find Shortest String Character Order

Problem statement

You are given N subsequences(not necessarily contiguous) of a string. Find the shortest possible string which has distinct lower case letters, with the given subsequences. The solution is guaranteed to exist. 

Input

The first line has the value of N, followed by N lines containing each of the N subsequences of the solution string.

Each subsequence has distinct lower case letters

1<=N<=100000

Output

Output the value of the solution string.

Example

Input:

2

acd

bc

Output:

abcd

second test case  

Input:

3

ac

dbe

dea

Output:

dbeac

void toposort(unordered_map<char,unordered_set<char>>& map, 
              unordered_map<char, bool>& visited, stack<char>& st, char c) {
    visited[c] = true;
    for(auto u:map[c]) {
        if(!visited.count(u))
            toposort(map, visited, st, u);
    }
    st.push(c);
}

string findOrder(vector<string>& strs) {
    unordered_map<char,unordered_set<char>> map;
    unordered_map<char, bool> visited;
    unordered_set<char> set;
    stack<char> st;
    for(auto& s:strs) {
        for(unsigned i=1; i<s.size(); i++) {
            map[s[i-1]].insert(s[i]);
            set.insert(s[i]);
        }
        set.insert(s[0]);
    }
    for(auto k:set) {
        if(!visited.count(k)) {
            toposort(map, visited, st, k);
        }
    }
    string res;
    while(!st.empty()) {
        res += st.top();
        st.pop();
    }
    return res;
}