PP numbers are prime numbers and palindromes in decimal notation at once. Your task is to find n-th PP number in ascending order. Then calculate product of its non-zero digits - let's call it m - and find m-th prime number in ascending order.

Input

In the first line of input there is one positive integer Z (1 ≤ Z ≤ 1000) which states the number of test cases. Following Z lines contain test cases.

Each test case consists of one positive integer n (1 ≤ n ≤ 113) which states the number of PP number to find.

Output

For each test case print in separate line two numbers: n-th PP number and m-th prime number.

Example

Input:
3
1
5
2

Output:
2 3
11 2
3 5