Dark is going to attend Motarack's birthday. Dark decided that the gift he is going to give to Motarack is an array $a$ of $n$ non-negative integers.
Dark created that array $1000$ years ago, so some elements in that array disappeared. Dark knows that Motarack hates to see an array that has two adjacent elements with a high absolute difference between them. He doesn't have much time so he wants to choose an integer $k$ ($0 \leq k \leq 10^{9}$) and replaces all missing elements in the array $a$ with $k$.
Let $m$ be the maximum absolute difference between all adjacent elements (i.e. the maximum value of $|a_i - a_{i+1}|$ for all $1 \leq i \leq n - 1$) in the array $a$ after Dark replaces all missing elements with $k$.
Dark should choose an integer $k$ so that $m$ is minimized. Can you help him?
-----Input-----
The input consists of multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 10^4$)  — the number of test cases. The description of the test cases follows.
The first line of each test case contains one integer $n$ ($2 \leq n \leq 10^{5}$) — the size of the array $a$.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($-1 \leq a_i \leq 10 ^ {9}$). If $a_i = -1$, then the $i$-th integer is missing. It is guaranteed that at least one integer is missing in every test case.
It is guaranteed, that the sum of $n$ for all test cases does not exceed $4 \cdot 10 ^ {5}$.
-----Output-----
Print the answers for each test case in the following format:
You should print two integers, the minimum possible value of $m$ and an integer $k$ ($0 \leq k \leq 10^{9}$) that makes the maximum absolute difference between adjacent elements in the array $a$ equal to $m$.
Make sure that after replacing all the missing elements with $k$, the maximum absolute difference between adjacent elements becomes $m$.
If there is more than one possible $k$, you can print any of them.
-----Example-----
Input
7
5
-1 10 -1 12 -1
5
-1 40 35 -1 35
6
-1 -1 9 -1 3 -1
2
-1 -1
2
0 -1
4
1 -1 3 -1
7
1 -1 7 5 2 -1 5
Output
1 11
5 35
3 6
0 42
0 0
1 2
3 4
-----Note-----
In the first test case after replacing all missing elements with $11$ the array becomes $[11, 10, 11, 12, 11]$. The absolute difference between any adjacent elements is $1$. It is impossible to choose a value of $k$, such that the absolute difference between any adjacent element will be $\leq 0$. So, the answer is $1$.
In the third test case after replacing all missing elements with $6$ the array becomes $[6, 6, 9, 6, 3, 6]$.  $|a_1 - a_2| = |6 - 6| = 0$;  $|a_2 - a_3| = |6 - 9| = 3$;  $|a_3 - a_4| = |9 - 6| = 3$;  $|a_4 - a_5| = |6 - 3| = 3$;  $|a_5 - a_6| = |3 - 6| = 3$. 
So, the maximum difference between any adjacent elements is $3$.
from math import *

zzz = int(input())
for zz in range(zzz):
    n = int(input())
    a = [int(i) for i in input().split()]
    b = set()
    for i in range(n):
        if a[i] == -1:
            if i > 0:
                if a[i-1] >= 0:
                    b.add(a[i-1])
            if i < n - 1:
                if a[i+1] >= 0:
                    b.add(a[i+1])
    b = list(b)
    if len(b) == 0:
        print(0, 0)
    else:
        k = (min(b) + max(b)) // 2
        m = 0
        for i in range(n):
            if a[i] == -1:
                a[i] = k
        for i in range(1, n):
            m = max(m, abs(a[i-1]- a[i]))
        print(m, k)

from math import *

zzz = int(input())
for zz in range(zzz):
    n = int(input())
    a = [int(i) for i in input().split()]
    b = set()
    for i in range(n):
        if a[i] == -1:
            if i > 0:
                if a[i-1] >= 0:
                    b.add(a[i-1])
            if i < n - 1:
                if a[i+1] >= 0:
                    b.add(a[i+1])
    b = list(b)
    if len(b) == 0:
        print(0, 0)
    else:
        k = (min(b) + max(b)) // 2
        m = 0
        for i in range(n):
            if a[i] == -1:
                a[i] = k
        for i in range(1, n):
            m = max(m, abs(a[i-1]- a[i]))
        print(m, k)
