A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

We define here a new prime number called prime of primes number (POP) is a prime number that consists of other prime numbers less than this number.

Example: 1013 consists of 101 and 3 and both are prime.

Notes: 2003 is not POP because leading zeros are not allowed.

The POP numbers must contain more than or equal two primes, and overlapping is not allowed .

Input

The first line contains an integer T specifying the number of test cases. (T <= 200)

Followed by T lines, each line contains an integer m number 0 <= m <= 10¹⁸.

Output

For each test case print single line contain the first integer greater than or equal to m and is (POP) .

Example

Input

3
10
100
1000

Output

23
113
1013

After solving this you can try http://www.spoj.com/problems/POP3/