Leapfrog

Frogs gather on the wide road that cuts through the forest. Whenever frogs meet at the same position, they climb on top of each other and form a tower.

Frog $i$ starts at position $x_i$ and moves exactly $d_i$ forward on every jump. Each $d_i$ is a prime, and a frog never jumps backwards, so frog $i$ can only stand at $x_i$, $x_i + d_i$, $x_i + 2 d_i$, $\dots$.

The size of the tower at position $p$ is the number of frogs that can reach $p$, that is the number of indices $i$ with $x_i \le p$ and $p - x_i$ divisible by $d_i$.

The frog king wants to present the largest tower. If several positions carry a tower of that largest size, he picks the smallest such position. Report that position and the size of the tower.

The first line contains the number of frogs $n$ ($1 \le n \le 40$).

Each of the next $n$ lines contains the start position $x_i$ and the jump distance $d_i$ of one frog, separated by a space ($0 \le x_i \le 2^{60}$, $2 \le d_i \le 10^8$).

Every $d_i$ is prime, and the product of all distinct jump distances is less than $10^9$.

Print one line with the smallest position that carries a largest tower and the size of that tower, separated by a space.