Finding the Prime Sum Range

Given an integer \(n\), find two integers \(l\) and \(r\) (with \(l \le r\)) such that the sum of all prime numbers in the interval \([l, r]\) equals \(n\). Formally, let \[ S(l, r) = \sum_{\substack{p\;\text{is prime}\\ l \le p \le r}} p, \] find \(l\) and \(r\) satisfying \(S(l, r) = n\).

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

inputFormat

The input consists of a single integer \(n\) (\(1 \le n \le 10^9\)).

outputFormat

If a valid interval is found, output two integers \(l\) and \(r\) separated by a space. Otherwise, output NIE.

sample

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