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.*;

public class Main {

	static long sx = 0, sy = 0, m = (long) (1e9 + 7);

	static ArrayList<Integer>[] a;
	static pair[][][][] dp;
	static long[] farr;
	// static boolean b = true;
	static HashMap<Integer, Integer> hm = new HashMap<>();

	// static TreeMap<Integer, Integer> hm = new TreeMap<>();
	public static PrintWriter out;
	static ArrayList<pair> ans = new ArrayList<>();
	static long[] fact = new long[(int) 1e6];
	static boolean b = false;
	static StringBuilder sb = new StringBuilder();
	static boolean cycle = false;
	static long mod = 998244353;
	static int[] col;
	static HashSet<Integer> p = new HashSet<>();
	static int cnt;

	public static void main(String[] args) throws IOException {

		Scanner scn = new Scanner(System.in);

		out = new PrintWriter(System.out);

		int t = scn.nextInt();

		z: while (t-- != 0) {

			StringBuilder ans = new StringBuilder();

			String s = scn.next();

			int[] a = preprocessLPS(s + "*" + reverse(s));

			int p = 0;

			for (int i = 1; i + s.length() < a.length; i++)
				if (a[s.length() + i] == i)
					p = i;

			for (int i = 0; i < p; i++)
				ans.append(s.charAt(i));

			if (p == s.length()) {
				System.out.println(s);
				continue z;
			}

			StringBuilder st = new StringBuilder(ans);
			st.reverse();                                  // suffix  == preifx

			String temp = s.substring(p, s.length() - p);

			StringBuilder sb = new StringBuilder(temp + "*" + reverse(temp));

			a = preprocessLPS(sb.toString());

			StringBuilder te = new StringBuilder();

			for (int i = 0; i < a[a.length - 1]; i++)
				te.append(temp.charAt(i));                  //longest palin prefix

			sb = new StringBuilder(reverse(temp) + "*" + temp);

			a = preprocessLPS(sb.toString());

			if (a[a.length - 1] > te.length()) {
				
				te = new StringBuilder();
				
				for (int i = 0; i < a[a.length - 1]; i++)
					te.append(temp.charAt(temp.length() - 1 - i));
			}

			ans.append(te);
			ans.append(st);

			System.out.println(ans);

		}

	}

	private static String reverse(String s) {

		return new StringBuilder(s).reverse().toString();
	}

	public static int[] preprocessLPS(String p) {

		int[] lps = new int[p.length()];
		int l = 0;
		int i = 1;

		while (i < lps.length) {

			if (p.charAt(l) == p.charAt(i)) {
				l++;
				lps[i] = l;
				i++;
			}

			else {
				if (l > 0)
					l = lps[l - 1];
				else
					i++;

			}
		}
		return lps;
	}

	// _________________________TEMPLATE_____________________________________________________________

	// private static int gcd(int a, int b) {
	// if (a == 0)
	// return b;
	//
	// return gcd(b % a, a);
	// }

	// static class comp implements Comparator<Integer> {
	//
	// @Override
	// public int compare(Integer o1, Integer o2) {
	// if (b[o1])
	// return -1;
	// else if (b[o2])
	// return 1;
	// else
	// return (int) (a[o2].size() - a[o1].size());
	// }
	//
	// }

	// public static long pow(long a, long b) {
	//
	// if(b<0)return 0;
	// if (b == 0 || b == 1)
	// return (long) Math.pow(a, b);
	//
	// if (b % 2 == 0) {
	//
	// long ret = pow(a, b / 2);
	// ret = (ret % mod * ret % mod) % mod;
	// return ret;
	// }
	//
	// else {
	// return ((pow(a, b - 1) % mod) * a % mod) % mod;
	// }
	// }

	private static class pair implements Comparable<pair> {

		String s;
		int len;

		pair(String a, int b) {
			s = a;
			len = b;
		}

		@Override
		public int compareTo(pair o) {

			return 1;
		}

	}

	public static class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

		public Reader() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public Reader(String file_name) throws IOException {
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String readLine() throws IOException {
			byte[] buf = new byte[1000000 + 1]; // line length
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}

		public int nextInt() throws IOException {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}

		public long nextLong() throws IOException {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}

		public double nextDouble() throws IOException {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();

			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (c == '.') {
				while ((c = read()) >= '0' && c <= '9') {
					ret += (c - '0') / (div *= 10);
				}
			}

			if (neg)
				return -ret;
			return ret;
		}

		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}

		private byte read() throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}

		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}

		public int[] nextIntArray(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) throws IOException {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		public int[][] nextInt2DArray(int m, int n) throws IOException {
			int[][] arr = new int[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}
		// kickstart - Solution
		// atcoder - Main
	}

}