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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Global7D {
	public static void main(String[] args) throws Exception {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter writer = new PrintWriter(System.out);
		int testCases = Integer.parseInt(reader.readLine());
		for (int tt = 0; tt < testCases; tt++) {
			String s = reader.readLine();
			int count = 0;
			for (int i = 0; i < s.length() / 2; i++) {
				if (s.charAt(i) == s.charAt(s.length() - i - 1)) {
					count++;
				} else {
					break;
				}
			}
			String x = get(s.substring(count, s.length() - count));
			writer.println(s.substring(0, count) + x + s.substring(s.length() - count, s.length()));
		}

		reader.close();
		writer.close();
	}
	public static String get(String text){
		int N = text.length();
		if (N == 0) {
			return "";
		} else if (N == 1) {
			return text;
		}
		N = 2 * N + 1; // Position count
		int[] L = new int[N + 1]; // LPS Length Array
		L[0] = 0;
		L[1] = 1;
		int C = 1; // centerPosition
		int R = 2; // centerRightPosition
		int i = 0; // currentRightPosition
		int iMirror; // currentLeftPosition
		int maxLPSLength = 0;
		int maxLPSCenterPosition = 0;
		int start = -1;
		int end = -1;
		int diff = -1;
		for (i = 2; i < N; i++) {
			iMirror = 2 * C - i;
			L[i] = 0;
			diff = R - i;
			if (diff > 0) {
				L[i] = Math.min(L[iMirror], diff);
			}
			while (((i + L[i]) + 1 < N && (i - L[i]) > 0) &&
					(((i + L[i] + 1) % 2 == 0) ||
							(text.charAt((i + L[i] + 1) / 2) ==
									text.charAt((i - L[i] - 1) / 2)))){
				L[i]++;
			}
			if (L[i] == i || i + L[i] == text.length() * 2) {
				if (L[i] > maxLPSLength)  {
					maxLPSLength = L[i];
					maxLPSCenterPosition = i;
				}
			}
			if (i + L[i] > R) {
				C = i;
				R = i + L[i];
			}
		}
		start = (maxLPSCenterPosition - maxLPSLength) / 2;
		end = start + maxLPSLength;
		return text.substring(start, end);
	}
	/*public static String get(String x) {
		// n ^ 2
		int maxLength = 0;
		String bestString = "";
		for (int i = 0; i < x.length(); i++) {
			int count = 0;
			while (i - count >= 0 && i + count < x.length() &&
					x.charAt(i - count) == x.charAt(i + count)) {
				count++;
			}
			if ((count - 1 == i) || (x.length() - i == count)) {
				int length = 2 * count - 1;
				if (length > maxLength) {
					maxLength = length;
					bestString = x.substring(i - count + 1, i + count);
				}
			}
		}
		for (int i = 0; i < x.length() - 1; i++) {
			int count = 0;
			while (i - count >= 0 && i + 1 + count < x.length() &&
					x.charAt(i - count) == x.charAt(i + 1 + count)) {
				count++;
			}
			if (i + 1 == count || x.length() - count - 1 == i) {
				int length = 2 * count;
				if (length > maxLength) {
					maxLength = length;
					bestString = x.substring(i - count + 1, i + count + 1);
				}
			}
		}
		return bestString;
	}*/
}