P10495 Factorization of a Factorial

Given an integer $N (3 \le N \le 10^6)$, factorize the factorial $N!$ into prime factors. You only need to output $p_i$ and $c_i$ in the form required by the Fundamental Theorem of Arithmetic.

An integer $N$.

The prime factorization result of $N!$, consisting of several lines. Each line contains a pair $p_i, c_i$, meaning there is a term $p_i^{c_i}$. Output in increasing order of $p_i$.

Translated by ChatGPT 5