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:
//package cf;
import java.io.*;
import java.util.*;

public class T_class {
    static int m=2147483647;
    static int p=1000000007;
    static int max=(int)2e3+10;
    static boolean prime[]=new boolean[max+5];
    static  int dp[][]=new int[(int)max][max];
    static  List<Integer> total_prime=new ArrayList<>();

    public static void main(String[] args) throws Exception {
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(FileDescriptor.out), "ASCII"), 512);
        FastReader sc=new FastReader();
        int t=sc.nextInt();
        StringBuilder sb2=new StringBuilder();

        while(t-- >0) {
            StringBuilder s=new StringBuilder();
            s.append(sc.nextLine());
            char ar[]=s.toString().toCharArray();
            int n=ar.length;
            int l=0,r=n-1;
            ArrayDeque<Character> q1=new ArrayDeque<>();
            ArrayDeque<Character> q2=new ArrayDeque<>();

            while(l<r&&ar[l]==ar[r])
            {
                q1.addLast(ar[l]);
                q2.addFirst(ar[r]);
                l++;
                r--;
            }
            if(l<=r)
            {
                char cpy[]=Arrays.copyOfRange(ar,l,r+1);
                String mid1=long_pre(cpy);
                int len=cpy.length;
              //  System.out.println(Arrays.toString(cpy));
                for(int i=0;i<len/2;i++)
                {
                    char temp=cpy[i];
                    cpy[i]=cpy[len-1-i];
                    cpy[len-1-i]=temp;
                }
              //  System.out.println(Arrays.toString(cpy));
                String mid2=long_pre(cpy);
         //      System.out.println(mid1+" "+mid2);
                mid1=mid1.length()>mid2.length()?mid1:mid2;
                    while(q1.isEmpty()==false)
                        sb2.append(q1.poll());
                sb2.append(mid1);
                while (q2.isEmpty()==false)
                    sb2.append(q2.pollFirst());
            }
            else
            {
                while(q1.isEmpty()==false)
                    sb2.append(q1.poll());
                while (q2.isEmpty()==false)
                    sb2.append(q2.pollFirst());
            }
            sb2.append("\n");
        }
        System.out.println(sb2.toString());
        out.flush();
    }
    public static long gethash(long pow[], long hash[], int l, int r) {

        return (hash[r+1] - (hash[l ] * pow[r - l +1]) % m + m) % m;
    }
    private static String long_pre(char[] ch) {
        int n=ch.length;
        char cpy[]=new char[n];
        for(int i=n-1;i>=0;i--)
        {
            cpy[n-1-i]=ch[i];
        }
        long pow[] = new long[n + 1];
        long hash[] = new long[n + 1];
        pow[0] = 1;
        int p = 31;
        for (int i = 1; i <= n; i++) {
            pow[i] = (pow[i - 1] % m * p % m) % m;
        }

        for (int i = 1; i <= n; i++) {
            hash[i] = (hash[i - 1] * p % m + (ch[i - 1]) % m) % m;
        }

        long pow1[] = new long[n + 1];
        long hash1[] = new long[n + 1];
        pow1[0] = 1;
        //int p = 31;
        for (int i = 1; i <= n; i++) {
            pow1[i] = (pow1[i - 1] % m * p % m) % m;
        }

        for (int i = 1; i <= n; i++) {
            hash1[i] = (hash1[i - 1] * p % m + (cpy[i - 1]) % m) % m;
        }


        int l=0,r=n-1,lst=0;
        for(int i=n-1;i>=1;i--)
        {
        int mid=i%2;
        int midp=i/2;
        if(mid==0&&gethash(pow,hash,0,midp-1)==gethash(pow1,hash1,n-1-i,n-1-(midp+1)))
        {
            lst=i;
            break;
        }
        else if(mid==1&&gethash(pow,hash,0,midp)==gethash(pow1,hash1,n-1-i,n-1-(midp+1)))
        {
            lst=i;
            break;
        }
        }
        StringBuilder sb=new StringBuilder();
        for(int i=0;i<=lst;i++)
        {
            sb.append(ch[i]);
        }
        return sb.toString();
    }

    private static int Solve(int n, int l, int r,int h, int i, int s, int[] ar) {
        if(i==n)
            return 0;
        if(dp[i][s]!=-1)
            return dp[i][s];

        int ans=Math.max(con((s+ar[i])%h,l,r)+Solve(n,l,r, h,i+1,(s+ar[i])%h,ar)
                ,con((s+ar[i]-1)%h,l,r)+Solve(n,l,r,h,i+1,(s+ar[i]-1+h)%h,ar));
        dp[i][s]=ans;
        return dp[i][s];
    }

    private static int con(int i,int l,int r) {
        if(l<=i&&i<=r)
            return 1;
        else
            return 0;
    }

    static  long childs[]=new long[max];
    static long tot=0;
    public static void dfs_val(List<Integer> adj[],int u,int p,long val) {
        int in_max=-1;
        val=val+childs[u]+1;
        for(int v:adj[u])
        {
            if(v!=p)
            {
                in_max=v;
                dfs_val(adj,v,p,val);
            }
        }
        if(in_max==-1)
        {
            tot=Math.max(tot,val);
        }
    }
    public static void dfs(List<Integer> adj[],int u,int p)
    {

        for(int v:adj[u])
        {
            if(v!=p)
            {
                childs[u]++;
                dfs(adj,v,u);
                childs[u]+=childs[v];
            }
        }
    }
    public static int ans(int ar[],int i,int n,int t)
    {
        if(i>=n)
            return 0;
        if(t>=410)
            return 200000;
        if(dp[i][t]!=-1)
            return dp[i][t];
        //System.out.println(t+" "+i);
        int cur=Math.min(Math.abs(ar[i]-t)+ans(ar,i+1,n,t+1),ans(ar,i,n,t+1));
        dp[i][t]=cur;
        return dp[i][t];
    }

    private static long ncr(int n, int r, long[] fact) {
        if(r>n||n < 0 || r < 0)
            return 0;

        if(n==1||n==0)
            return 1;
        // System.out.println(n+" c "+r);

        return (((fact[n]*pow_inverse(fact[n-r],p))%p)*pow_inverse(fact[r],p))%p;
    }
    static class BIT {
        long[] tree;
        public BIT(int size) {
            tree = new long[size + 1];
        }
        public long sum(int i) {
            long ans = 0;
            while (i > 0) {
                ans += tree[i];
                i -= i & -i;
            }
            return ans;
        }

        public long query(int i, int j) {
            return sum(j) - sum(i - 1);
        }

        public void add(int i, long val) {
            while (i < tree.length) {
                tree[i] += val;
                i += i & -i;
            }
        }

        public void set(int i, long val) {
            add(i, val - query(i, i));
        }
    }
    static class  vert implements Comparator<vert>
    {
        int v;
        TreeSet<Integer> set;

        public vert(int v, TreeSet<Integer> set) {
            this.v = v;
            this.set = set;
        }

        @Override
        public int compare(vert o1, vert o2) {
            return -(o1.set.size()-o2.set.size());
        }
    }
    public static long pow(long a,long b,long m)
    {
        long r=1;
        while(b!=1)
        {
            if(b%2!=0)
                r=(r*a)%m;
            b=b>>1;
            a=(a*a)%m;
        }
        return (r*a)%m;
    }
    public static long pow_inverse(long a,long m)
    {
        return pow(a,m-2,m);
    }public static long gcd(long a,long b)
    {
        if(b>a)
        {
            a=a^b;
            b=a^b;
            a=a^b;
        }
        if(b==0)
            return a;
        return gcd(b,a%b);
    }
    public static void extgcd(long a,long b)
    {/*
            if(a==0)
            {
                x=0;
                y=1;
                d=b;
                // return ;
            }
            else
            {

                extgcd(b%a,a);

                long t=y;
                y=x;
                x=t-(b/a)*x;
            }*/
    }

    public static void seive()
    {
        for(int i=0;i<max;i++)
            prime[i] = true;

        for(int p = 2; p*p <=max; p++)
        {
            // If prime[p] is not changed, then it is a prime
            if(prime[p] == true)
            {
                // Update all multiples of p
                for(int i = p*p; i <=max; i += p)
                    prime[i] = false;
            }
        }

        // Print all prime numbers
        for(int i = 2; i <= max; i++)
        {
            if(prime[i] == true)
            {
                total_prime.add(i);
            }
        }
    }
    public static boolean union(int a, int b, int p[], int r[]){
        // add your code here
        int pa=find(a,p,r);
        int pb=find(b,p,r);
        if(pa==pb)
            return true;
        if(pa!=pb)
        {
            if(r[pa]<r[pb])
            {
                p[pa]=pb;
            }
            else if(r[pa]>r[pb])
            {
                p[pb]=pa;
            }
            else
            {
                p[pa]=pb;
                r[pb]++;
            }
        }
        return false;
    }
    public static int find(int x,int p[],int r[])
    {
        if(p[x]==x)
            return x;
        p[x]=find(p[x],p,r);
        return p[x];
    }
    public static int binary_Search_upper(Integer[] ar, Integer x,int l,int r)
    {
        int res=-1,f=0;
        while(l<=r)
        {
            int mid=(l+r)>>1;
            if(ar[mid]==x)
            {
                f=1;
                res=mid;
                l=mid+1;
            }
            else if(ar[mid]>x)
            {
                res=res!=-1&&ar[res]==x?res:mid;
                r=mid-1;
            }
            else
            {
                l=mid+1;
            }
        }
        return f==1?res:res+1;
    }
    public static int binary_Search_lower(int[] ar, long x, int l, int r)
    {
        int res=0,f=0;
        //int l=0;int r=ar.length-1;
        /*public static int binary(Long[] ar, int l, int r, long v)
        {
            int n=r;
            int m=(l+r)/2;
            int re=-1;
            while(l<=r)
            {
                if(ar[m]>=v)
                {

                    re=m;
                    r=m-1;
                }
                else if(ar[m]<v)
                {
                    l=m+1;
                }
                m=(l+r)/2;
            }
            if(l<=n&&ar[l]==v)
                return l;
            return re;
        }*/
        //   System.out.println(Arrays.toString(ar)+" "+x);
        while(l<=r)
        {
            int mid=(l+r)>>1;
            //   System.out.println(l+" "+r+" "+mid+" = "+ar[mid]);
            if(ar[mid]==x)
            {
                f=1;
                res=mid;
                r=mid-1;
            }
            else if(ar[mid]>x)
            {
                r=mid-1;
            }
            else
            {
                res=res!=0&&ar[res]==x?res:mid;
                l=mid+1;
            }
        }

        //  System.out.println(res);
        return f==1?res:res+1;
    } public static int binary_Search_lower_suf(int[] ar, int x,int l,int r)
    {
        int res=-1,f=0;
        //int l=0;int r=ar.length-1;
        while(l<=r)
        {
            int mid=(l+r)>>1;
            if(ar[mid]==x)
            {
                f=1;
                res=mid;
                r=mid-1;
            }
            else if(ar[mid]<x)
            {
                r=mid-1;
            }
            else
            {
                //      res=mid;
                l=mid+1;
            }
        }
        return f==0?res+1:res;
    }
    int bit[]=new int[(int)1e6];
    public void update(int n,int val,int i)
    {
        i++;
        while(i<n)
        {
            bit[i]+=val;
            i+=(i)&(-i);
        }

    }
    public long query(int n,int i)
    {
        i++;
        long sum=0;
        while(i>0)
        {
            sum+=bit[i];
            i-=(i)&(-i);
        }
        return sum;
    }


    ///////////////////////////////////////////////////////////////////////////////////
    //////////////////////////////////////////////////////////////////////////////////////////////
    static class FastReader {

        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }


}