Yes, Prime Minister

Mr. Hacker's Department of Administrative Affairs (DAA) has infinite civil servants. Every integer is used as an id number by exactly one civil servant. Mr. Hacker is keen on reducing overmanning in civil service, so he will only keep people with consecutive id numbers in $[l,r]$ and dismiss others.

However, permanent secretary Sir Humphrey's id number is $x$ and he cannot be kicked out so there must be $l \leq x \leq r$. Mr. Hacker wants to be Prime Minister so he demands that the sum of people's id number $\sum_{i=l}^r i$ must be a prime number.

You, Bernard, need to make the reduction plan which meets the demands of both bosses. Otherwise, Mr. Hacker or Sir Humphrey will fire you.

Mr. Hacker would be happy to keep as few people as possible. Please calculate the minimum number of people left to meet their requirements.

A prime number $p$ is an integer greater than $1$ that has no positive integer divisors other than $1$ and $p$.

The first line contains an integer $T(1 \leq T \leq 10^6)$ - the number of test cases. Then $T$ test cases follow.

The first and only line of each test case contains one integer $x_i (-10^7 \leq x_i \leq 10^7)$ - Sir Humphrey's id number.

For each test case, you need to output the minimal number of people kept if such a plan exists, output $-1$ otherwise.

10
-2
-1
0
1
2
3
4
5
6
7

6
4
3
2
1
1
2
1
2
1

2021“MINIEYE杯”中国大学生算法设计超级联赛（6）