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 $3$.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'for _ in range(int(input())):\n    n = int(input())\n    ans = 0\n    adj = []\n    a = tuple(map(int, input().split()))\n    a1 = iter(a)\n    next(a1)\n    for ai, aj in zip(a, a1):\n        if ai > -1 < aj:\n            ans = max(ans, abs(ai - aj))\n        elif ai != aj:\n            adj.append(ai + aj + 1)\n    min_adj, max_adj = (min(adj), max(adj)) if adj else (0, 0)\n    print(max(ans, (max_adj - min_adj + 1) // 2), (min_adj + max_adj) // 2)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13309