Problem: This is the hard version of the problem. The difference is the constraint on the sum of lengths of strings and the number of test cases. You can make hacks only if you solve all versions of this task.

You are given a string s, consisting of lowercase English letters. Find the longest string, t, which satisfies the following conditions: 

  * The length of t does not exceed the length of s. 
  * t is a palindrome. 
  * There exists two strings a and b (possibly empty), such that t = a + b ( "+" represents concatenation), and a is prefix of s while b is suffix of s. 

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^5), the number of test cases. The next t lines each describe a test case.

Each test case is a non-empty string s, consisting of lowercase English letters.

It is guaranteed that the sum of lengths of strings over all test cases does not exceed 10^6.

Output

For each test case, print the longest string which satisfies the conditions described above. If there exists multiple possible solutions, print any of them.

Example

Input


5
a
abcdfdcecba
abbaxyzyx
codeforces
acbba


Output


a
abcdfdcba
xyzyx
c
abba

Note

In the first test, the string s = "a" satisfies all conditions.

In the second test, the string "abcdfdcba" satisfies all conditions, because:

  * Its length is 9, which does not exceed the length of the string s, which equals 11. 
  * It is a palindrome. 
  * "abcdfdcba" = "abcdfdc" + "ba", and "abcdfdc" is a prefix of s while "ba" is a suffix of s. 



It can be proven that there does not exist a longer string which satisfies the conditions.

In the fourth test, the string "c" is correct, because "c" = "c" + "" and a or b can be empty. The other possible solution for this test is "s".

Solution (in JAVA):

Solution:

import java.io.*;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;
 
public  class realfast implements Runnable 
  {
    private static final int INF = (int) 1e9;
    long in= (long)Math.pow(10,9)+7;
    long fac[]= new long[3000];
    public  void solve() throws IOException 
    {
     int t = readInt();
     for(int f =0;f<t;f++)
     {
        String s = readString();
        int len=0;
        for(int i =0;i<s.length()/2;i++)
        {
             if(s.charAt(i)!=s.charAt(s.length()-1-i))
             {
                break;
             }
             len++;
        }
        //out.println(len);
        String par = s.substring(len,s.length()-len);

        char po[]= new char[2*par.length()+1];
        char lo[]= new char[2*par.length()+1];
        for(int i =0;i<par.length();i++)
        {
          po[i]=par.charAt(i);
          po[po.length-i-1]=par.charAt(i);
          lo[par.length()-i-1]=par.charAt(i);
          lo[par.length()+i+1]=par.charAt(i);
        }
        po[par.length()]='#';
        lo[par.length()]='#';
        int ppo[]= computeTemporaryArray(po);
        int lpo[]= computeTemporaryArray(lo);
        if(ppo[2*par.length()]>lpo[2*par.length()])
        {
            String pre = s.substring(0,len);
            String suf= s.substring(s.length()-len,s.length());
            String mid = par.substring(0,ppo[2*par.length()]);
            out.println(pre+mid+suf);
        }
        else
        {
            String pre = s.substring(0,len);
            String suf= s.substring(s.length()-len,s.length());
            String mid = par.substring(par.length()-lpo[2*par.length()],par.length());
            out.println(pre+mid+suf);

        }
     }
     

    }
    public int[] computeTemporaryArray(char pattern[]){

        int [] lps = new int[pattern.length];

        int index =0;

        for(int i=1; i < pattern.length;){

            if(pattern[i] == pattern[index]){

                lps[i] = index + 1;

                index++;

                i++;

            }else{

                if(index != 0){

                    index = lps[index-1];

                }else{

                    lps[i] =0;

                    i++;

                }

            }

        }
       // for(int i =0;i<lps.length;i++)
         //   out.print(lps[i]+" ");
        //out.println();

        return lps;

    }
    ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
    public static void main(String[] args) {
        new Thread(null, new realfast(), "", 128 * (1L << 20)).start();
    }
 
    private static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    private BufferedReader reader;
    private StringTokenizer tokenizer;
    private PrintWriter out;
 
    @Override
    public void run() {
        try {
            if (ONLINE_JUDGE || !new File("input.txt").exists()) {
                reader = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                reader = new BufferedReader(new FileReader("input.txt"));
                out = new PrintWriter("output.txt");
            }
            solve();
        } catch (IOException e) {
            throw new RuntimeException(e);
        } finally {
            try {
                reader.close();
            } catch (IOException e) {
                // nothing
            }
            out.close();
        }
    }
 
    private String readString() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
 
    @SuppressWarnings("unused")
    private int readInt() throws IOException {
        return Integer.parseInt(readString());
    }
 
    @SuppressWarnings("unused")
    private long readLong() throws IOException {
        return Long.parseLong(readString());
    }
 
    @SuppressWarnings("unused")
    private double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }
}
class edge implements Comparable<edge>{
    int u ;
    int v ;
    int val;
    edge(int u1, int v1 , int val1)
    {
       this.u=u1;
       this.v=v1;
       this.val=val1;
    }
    public int compareTo(edge e)
    {
        return this.val-e.val;
    }
}