Problem Description

Given a number \( n \), find \( l \) and \( r \) such that the sum of all prime numbers in the interval \([l, r]\) equals \( n \).

If there are multiple solutions, any one of them is acceptable; if there is no solution, output NIE.

Input Format

A single line containing a positive integer \( n \).

Output Format

If there is a solution, output two positive integers \( l \) and \( r \) on a single line.

If there is no solution, output NIE.

Sample Input and Output

Sample Input #1

15

Sample Output #1

3 7

Sample Input #2

9992

Sample Output #2

4993 4999

Sample Input #3

100000000

Sample Output #3

NIE

Sample Input #4

1000000007

Sample Output #4

1000000007 1000000007

Sample Input #5

99999999996

Sample Output #5

295693 1693067

Notes

For all test cases, \( 1 \leq n \leq 10^{11} \).

见题面 Input 部分

见题面 Output 部分