Cloud of Hashtags （模拟暴力）

Vasya is an administrator of a public page of organization "Mouse and keyboard" and his everyday duty is to publish news from the world of competitive programming. For each news he also creates a list of hashtags to make searching for a particular topic more comfortable. For the purpose of this problem we define hashtag as a string consisting of lowercase English letters and exactly one symbol '#' located at the beginning of the string. The length of the hashtag is defined as the number of symbols in it without the symbol '#'.

The head administrator of the page told Vasya that hashtags should go in lexicographical order (take a look at the notes section for the definition).

Vasya is lazy so he doesn't want to actually change the order of hashtags in already published news. Instead, he decided to delete some suffixes (consecutive characters at the end of the string) of some of the hashtags. He is allowed to delete any number of characters, even the whole string except for the symbol '#'. Vasya wants to pick such a way to delete suffixes that the total number of deleted symbols is minimum possible. If there are several optimal solutions, he is fine with any of them.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 500 000) — the number of hashtags being edited now.

Each of the next n lines contains exactly one hashtag of positive length.

It is guaranteed that the total length of all hashtags (i.e. the total length of the string except for characters '#') won't exceed 500 000.

Output

Print the resulting hashtags in any of the optimal solutions.

Examples

Input

3
#book
#bigtown
#big

Output

#b
#big
#big

Input

3
#book
#cool
#cold

Output

#book
#co
#cold

Input

4
#car
#cart
#art
#at

Output

#
#
#art
#at

Input

3
#apple
#apple
#fruit

Output

#apple
#apple
#fruit

Note

Word a ₁, a ₂, ..., a _m of length m is lexicographically not greater than word b ₁, b ₂, ..., b _k of length k, if one of two conditions hold:

• at first position i, such that a _i ≠ b _i, the character a _i goes earlier in the alphabet than character b_i, i.e. a has smaller character than b in the first position where they differ;
• if there is no such position i and m ≤ k, i.e. the first word is a prefix of the second or two words are equal.

The sequence of words is said to be sorted in lexicographical order if each word (except the last one) is lexicographically not greater than the next word.

For the words consisting of lowercase English letters the lexicographical order coincides with the alphabet word order in the dictionary.

According to the above definition, if a hashtag consisting of one character '#' it is lexicographically not greater than any other valid hashtag. That's why in the third sample we can't keep first two hashtags unchanged and shorten the other two.

 

题意：将N个字符串序列通过删除最小的后缀来达到按字典序排序

题解：逆向暴力比较+优化

　　从1 -> N的话，可能存在第 J 个序列小于第 i 个序列（i<J），那么我们就要从新将上面的更新一下，这样太麻烦而且每次向上更新会导致T掉

　　逆向的话，每次向上更新的时候，下面的字符序列一定严格小于当前的序列，也就是每次只需要向上更新一次，不会T，over

 

#include <iostream>
#include <algorithm>
#include <cstring>
#include <string>
#include <vector>
#include <map>
#include <set>
#include <list>
#include <deque>
#include <queue>
#include <stack>
#include <cstdlib>
#include <cstdio>
#include <cmath>
#include <iomanip>
#define ull unsigned long long
#define ll long long
#define pb push_back
#define all(vc) vc.begin() , vc.end()
#define rep(i,start,end) for(int i=start;i<=end;i++)
#define per(i,end,start) for(int i=end;i>=start;i--)
#define tle ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define lc now<<1
#define rc now<<1|1
ll read()
{
    ll x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
using namespace std;
const int mod = 998244353;
const int mxn = 500000 +7;
ll _,n,m,t,k,u,v,ans,cnt,ok,lim,len,tmp;
ll  a[mxn] ,inv[mxn],lazy[mxn],id[mxn];
string str[mxn] , s1 ,s2;
int main()
{
    tle;
    while(cin>>n)
    {
        for(int i=1;i<=n;i++) cin>>str[i];
        for(int i=n-1;i>=1;i--)
        {
            int k = 1 , j = 1 ; ok = 0 ;
            if(str[i+1].size()==1)
            {
                str[i].erase(k);
                continue;
            }
            while( k<str[i].size() && j<str[i+1].size() )
            {
                if(str[i][k]==str[i+1][j]) k++,j++;
                else if(str[i][k]<str[i+1][j])
                {
                    ok = 1 ;
                    break;
                }
                else
                {
                    str[i].erase(k);
                    ok = 1 ;
                    break;
                }
            }
            if(k==j && j==str[i+1].size())
                str[i].erase(k);
        }
        for(int i=1;i<=n;i++)
            cout<<str[i]<<endl;
    }
}