Student ID Numbers

Every student entering Z University receives a student ID number. Each ID is an integer between $0$ and $10^6 - 1$ inclusive, and no two students share the same ID.

Professor Sang-geun Kim tells his students apart by their ID numbers. To remember them more easily, he wants to find the smallest positive integer $m$ such that, when every student's ID is divided by $m$, all of the resulting remainders are distinct.

For each test case, determine this smallest $m$.

The first line contains the number of test cases $N$.

Each test case begins with a line containing the number of students $G$ that the professor teaches ($1 \le G \le 300$). The next $G$ lines each contain one student's ID. No two students have the same ID.

For each test case, print on its own line the smallest positive integer $m$ such that all of the students' IDs give distinct remainders when divided by $m$.