A natural number $n$ that has exactly two distinct divisors, 1 and $n$, is called a prime number. For example, 6 is not a prime number (as it is divisible by 2), 1 is not a prime number (as it has only one divisor, 1), but 2 and 7 are prime numbers.

Bajtazar is very fond of prime numbers. He has written down a sequence of consecutive prime numbers on a piece of paper: $2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 \dots$

He would like to choose a contiguous fragment from this sequence whose sum is equal to his favorite number $N$. Help him and write a program that, for a given number $N$, finds any contiguous interval in the sequence of prime numbers whose sum is exactly $N$.

Input

The first and only line of input contains a single natural number $N$ ($1 \le N \le 10^{11}$) representing the sum expected by Bajtazar.

Output

The first and only line of output should contain two prime numbers $L$ and $R$ ($1 \le L \le R \le N$) such that the sum of prime numbers in the closed interval $[L, R]$ is exactly $N$.

If there are multiple solutions, your program may output any one of them. If no solution exists, you should output only the single word NIE.

Evaluation tests

• Test 1: $N = 9992$; output: $4993\ 4999$
• Test 2: $N = 10^8$; output: NIE
• Test 3: $N = 10^9 + 7$; output: $10^9 + 7\ 10^9 + 7$
• Test 4: $N = 10^{11} - 4$; output: $295693\ 1693067$

Examples

Input 1

15

Output 1

3 7

Subtasks

The test set is divided into the following subtasks. Tests for each subtask consist of one or more separate test groups.