23179번 - Periodic Ruler 다국어

Hitagi has a ruler of infinite length. It has a mark on every integer, where the mark on integer $i$ has color $c_i$. Each color is represented by an integer from $1$ to $100$.

She noticed that the ruler's color pattern repeats with a period of $t$. The period $t$ is defined by the smallest positive integer that satisfies $c_i = c_{i+t}$ for all integers $i$.

Hitagi told Koyomi the colors of $n$ marks of her choice. Koyomi wants to find all positive integers that cannot be a period of the ruler, regardless of the colors of unchosen marks. Write a program to find all such numbers, and output their count and sum.

The first line contains a single integer $n\ (1 \le n \le 50)$.

The following $n$ lines each contain two integers $x_i\ (|x_i| \le 10^9)$ and $a_i\  (1 \le a_i \le 100)$. This indicates that the integer $x_i$ is marked with the color $a_i$.

If $i \neq j$, then $x_i \neq x_j$.

Output two integers on one line. The first integer is the number of positive integers that cannot be the period of the ruler. The second integer is their sum.