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;
}