A Palindromic number is a number without leading zeros that remains the same when its digits are reversed. For instance 5, 22, 12321, 101101 are Palindromic numbers where as 10, 34, 566, 123421 are not. A Prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself. For example, 2, 31, 97 are Prime numbers but 1, 10, 25, 119 are not. A Palindromic Prime number is both palindromic and prime at the same time. 2, 3, 131 are Palindromic Prime numbers but 6, 17, 3333 are not. Given a positive integer N, output the largest palindromic prime number not greater than N. 

Input

The first line contains an integer T denoting the number of test cases. Each of the subsequent T lines contain a single integer N without leading/trailing spaces. 

Output

Print T lines. For each test case, print a single integer denoting the largest palindromic prime number which does not exceed N. 

Constraints

1 ≤ T ≤ 10^6

2 ≤ N ≤ 10^13

Example

Input:
3
2
10
666
Output:
2
7
383

Note
Large input and output, please use faster I/O methods.