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".
import java.util.*;
import java.io.*;
public class Main {
    static class Scan {
        private byte[] buf=new byte[1024];
        private int index;
        private InputStream in;
        private int total;
        public Scan()
        {
            in=System.in;
        }
        public int scan()throws IOException
        {
            if(total<0)
            throw new InputMismatchException();
            if(index>=total)
            {
                index=0;
                total=in.read(buf);
                if(total<=0)
                return -1;
            }
            return buf[index++];
        }
        public int scanInt()throws IOException
        {
            int integer=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n))
            {
                if(n>='0'&&n<='9')
                {
                    integer*=10;
                    integer+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            return neg*integer;
        }
        public double scanDouble()throws IOException
        {
            double doub=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n)&&n!='.')
            {
                if(n>='0'&&n<='9')
                {
                    doub*=10;
                    doub+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            if(n=='.')
            {
                n=scan();
                double temp=1;
                while(!isWhiteSpace(n))
                {
                    if(n>='0'&&n<='9')
                    {
                        temp/=10;
                        doub+=(n-'0')*temp;
                        n=scan();
                    }
                    else throw new InputMismatchException();
                }
            }
            return doub*neg;
        }
        public String scanString()throws IOException
        {
            StringBuilder sb=new StringBuilder();
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            while(!isWhiteSpace(n))
            {
                sb.append((char)n);
                n=scan();
            }
            return sb.toString();
        }
        private boolean isWhiteSpace(int n)
        {
            if(n==' '||n=='\n'||n=='\r'||n=='\t'||n==-1)
            return true;
            return false;
        }
    }
    static long p1,p_inv1,m1;
    static long p2,p_inv2,m2;
    static long pow1[], pow2[];
    public static void main(String args[]) throws IOException {
        Scanner input=new Scanner(System.in);
        
        p1=131;
        m1=951231973;
        p_inv1=Inverse(p1,m1);
        
        p2=167;
        m2=1000000007;
        p_inv2=Inverse(p2,m2);
        //Calculating power (p^n%)m
        pow1=new long[1000000];
        pow1[0]=1;
        
        pow2=new long[1000000];
        pow2[0]=1;
        for(int i=1;i<pow1.length;i++) {
            pow1[i]=pow1[i-1]*p1;
            pow1[i]%=m1;
            
            pow2[i]=pow2[i-1]*p2;
            pow2[i]%=m2;
        }
        
        int test=input.nextInt();
        StringBuilder ans=new StringBuilder("");
        for(int t=1;t<=test;t++) {
            String str=input.next();
            ans.append(solve(str.length(),str)+"\n");
        }
        System.out.println(ans);
    }
    public static String solve(int n,String str) {

        StringBuilder tmp=new StringBuilder(""+str);
        tmp=tmp.reverse();
        
        int len=0;
        for(int i=0,j=n-1;i<j;i++,j--) {
            if(str.charAt(i)!=str.charAt(j)) {
                break;
            }
            len=(i+1);
        }
        if(len==n) {
            return str;
        }
        int l1=longest_pal_prefix(str,len,n-len-1);
        int l2=longest_pal_prefix(""+tmp,len,n-len-1);
        StringBuilder ans=new StringBuilder("");
        for(int i=0;i<len;i++) {
            ans.append(str.charAt(i));
        }
        if(l1!=0 && l1>=l2) {
            for(int i=len;i<len+l1;i++) {
                ans.append(str.charAt(i));
            }
        }
        else if(l2!=0 && l2>l1){
            for(int i=n-len-l2;i<n-len;i++) {
                ans.append(str.charAt(i));
            }
        }
        for(int i=n-len;i<n;i++) {
            ans.append(str.charAt(i));
        }
//        System.out.println(ans);
        return ""+ans;
//        System.out.println(longest_pal_prefix+" "+longest_pal_suffix+" "+len);
    }
    public static int longest_pal_prefix(String str,int l,int r) {
        long hash1=0,rev_hash1=0;
        long hash2=0,rev_hash2=0;
        int max=0;
        for(int i=l,j=0;i<=r;i++,j++) {
            hash1+=(str.charAt(i)*pow1[j])%m1;
            hash1%=m1;
            rev_hash1*=p1;
            rev_hash1%=m1;
            rev_hash1+=str.charAt(i);
            rev_hash1%=m1;
            
            
            hash2+=(str.charAt(i)*pow2[j])%m2;
            hash2%=m2;
            rev_hash2*=p2;
            rev_hash2%=m2;
            rev_hash2+=str.charAt(i);
            rev_hash2%=m2;
            
            
            if(hash1==rev_hash1 && hash2==rev_hash2) {
                max=j+1;
            }
        }
//        System.out.println(l+" "+r+" "+max);
        return max;
    }
    
    public static long Inverse(long a,long n) {
        long q,r1=n,r2=a,r,t1=0,t2=1,t;
        while(true) {
            q=r1/r2;
            r=r1%r2;
            t=t1-(q*t2);
            r1=r2;
            r2=r;
            t1=t2;
            t2=t;
            if(r2==0) {
                    break;
            }
        }
        if(r1!=1) {
                return -1;
        }
        t1%=n;
        if(t1<0) {
                t1+=n;
        }
        return t1;
    }
}
