Chef And Babla Codechef Solution

Problem

Chef gives an array $A$ with $N$ elements to Babla. Babla’s task is to find the maximum non-negative integer $X$ such that:

• No element in the array belongs to the range $[-X,X]$. In other words, for all $(1\le i\le N)$, either ��<−�Ai​<−X or ��>�Ai​>X.

Help Babla to find the maximum non-negative integer $X$ for which the given condition is satisfied or determine if no such $X$ exists.

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• Each test case consists of multiple lines of input.
  • The first line of each test case contains an integer $N$ — the number of elements in the array.
  • The second line of each test case contains $N$ space-separated integers �1,�2,…,��A1​,A2​,…,AN​ representing the array $A$.

Output Format

For each test case, output on a new line, the maximum non-negative integer $X$, satisfying the above condition.
If no such $X$ exists, output $-1$ instead.

Constraints

Sample 1:

3
5
8 4 2 5 2
6
7 9 -10 8 12 17
4
0 -3 -1 -10

1
6
-1

Explanation:

Test case $1$: The maximum value of $X$ such that no element of the array belongs to the range $[-X,X]$ is $1$. All elements of the array are strictly greater than $1$.

Test case $2$: The maximum value of $X$ such that no element of the array belongs to the range $[-X,X]$ is $6$. All positive elements of the array are strictly greater than $6$ and negative elements are strictly less than $-6$.

Test case $3$: It is not possible to choose an element $X$ that satisfies the given condition.