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 ≤ k ≤ 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 ≤ i ≤ 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 ≤ t ≤ 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 ≤ n ≤ 10^{5}) — the size of the array a.

The second line of each test case contains n integers a_1, a_2, …, a_n (-1 ≤ a_i ≤ 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 ⋅ 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 ≤ k ≤ 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 ≤ 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.
import java.awt.*;
import java.io.*;
import java.io.IOException;
import java.util.*;
import java.text.DecimalFormat;
 
public class Codeforces {
	
	public static long mod = (long)Math.pow(10, 9)+7 ;
	public static double epsilon=0.00000000008854;//value of epsilon
	public static InputReader sc = new InputReader(System.in);
	public static PrintWriter pw = new PrintWriter(System.out);
	public static long gcd(long a,long b){
		while(b>0){
			long t=b;
			b=a%b;
			a=t;
		}
		return a;
    }
	
	static void dfs(Point p[],int v,boolean vis[]){
        if (vis[v])return;
        vis[v]=true;
        for (int i=0;i<p.length;i++){
            if (p[i].x==p[v].x || p[i].y==p[v].y){
                dfs(p,i,vis);
            }
        }
	}
	public static long bSearch(Pair[]d, int l, int r, int a) {
		if(d[l].d > a)
			return 0;
		if(l == r)
			return d[l].g;
		int m = (l + r + 1) / 2;
		if(d[m].d > a)
			return bSearch(d, l, m - 1, a);
		return bSearch(d, m, r, a);
	}
	static class Pair implements Comparable<Pair> {
		int d, i;
		long g;
		public Pair(int D, long G, int I) {
			d = D;
			g = G;
			i = I;
		}
		public int compareTo(Pair p) {
			if(d == p.d)
				return i - p.i;
			return d - p.d;
		}
	 }
	 
	 static void dfs(int src, ArrayList<ArrayList<Integer>> list, int vis[],int c[])
    {
        //Here 0-white,1-gray & 2-black;
       // Time complexity O(n+m)
       //System.out.print(src+" ");
	   vis[src]=1;
       for(int i=0;i<list.get(src).size();i++){
           if(vis[list.get(src).get(i)]==0){
               dfs(list.get(src).get(i),list, vis,c);
           }
	   }
	   c[0]++;
       vis[src]=2;
    }
	public static long pow(long x,long y,long mod){
		long ans=1;
		while(y>0){
			if((y&1)==1){
				ans=(ans*x)%mod;
			}
			y=y>>1;
			x=(x*x)%mod;
		}
		return ans;
    } 
	 
	public static void main(String[] args) {
		// code starts..
			int q=sc.nextInt();
			while(q-->0){
				int n=sc.nextInt();
				int a[]=scanArray(n);
				HashSet<Integer> h=new HashSet<>();
				int max=0;int min=Integer.MAX_VALUE;
				for(int i=0;i<n;i++){
					if(a[i]==-1)
					continue;
					if(i>0&&a[i-1]==-1){
						if(!h.contains(a[i])){
							min=Math.min(a[i], min);
							max=Math.max(a[i], max);
						}
						h.add(a[i]);

					}
					if(i+1<n&&a[i+1]==-1){
						if(!h.contains(a[i])){
							min=Math.min(a[i], min);
							max=Math.max(a[i], max);
						}
						h.add(a[i]);
					}
				}

				int avg=(max+min)/2;
				int max1=0,max2=0;
				int b[]=a.clone();
				for(int i=0;i<n;i++){
					if(a[i]==-1)
					a[i]=(int)avg;
				}
				for(int i=1;i<n;i++){
					max1=Math.max(Math.abs(a[i]-a[i-1]), max1);
				}
				
				pw.println(max1+" "+avg);
				//else pw.println(max2+" "+(avg+1));


			}

		// Code ends...
		pw.flush();
		pw.close();
	}
	static class tripletL implements Comparable<tripletL> {
		Long x, y, z;
 
		tripletL(long x, long y, long z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}
 
		public int compareTo(tripletL o) {
			int result = x.compareTo(o.x);
			if (result == 0)
				result = y.compareTo(o.y);
			if (result == 0)
				result = z.compareTo(o.z);
 
			return result;
		}
 
		public boolean equlas(Object o) {
			if (o instanceof tripletL) {
				tripletL p = (tripletL) o;
				return (x - p.x == 0) && (y - p.y ==0 ) && (z - p.z == 0);
			}
			return false;
		}
 
		public String toString() {
			return x + " " + y + " " + z;
		}
 
		public int hashCode() {
			return new Long(x).hashCode() * 31 + new Long(y).hashCode() + new Long(z).hashCode();
		}
	}
	public static String Doubleformate(double a,int n){
		String s="";
		while(n-->0){
			s+='0';
		}
		DecimalFormat f =new DecimalFormat("#0."+s);
		return f.format(a);
	}
 
	public static Comparator<Integer[]> column(int i){
		return 
		new Comparator<Integer[]>() {
			@Override
			public int compare(Integer[] o1, Integer[] o2) {
				return o1[i].compareTo(o2[i]);//for ascending
				//return o2[i].compareTo(o1[i]);//for descending
			}
		};
	}
	public static Comparator<Integer[]> pair(){
		return 
		new Comparator<Integer[]>() {
			@Override
			public int compare(Integer[] o1, Integer[] o2) {
				int result=o1[0].compareTo(o2[0]);
				if(result==0)
				result=o1[1].compareTo(o2[1]);
				return result;
			}
		};
	}
	public static Comparator<Integer[]> Triplet(){
		return 
		new Comparator<Integer[]>() {
			@Override
			public int compare(Integer[] o1, Integer[] o2) {
			
					for(int i=0;i<3;i++){
						for(int j=i+1;j<3;j++){
							for(int k=0;k<3;k++){
								for(int p=k+1;p<3;p++){
									if((o1[i]==o2[k]&&o1[j]==o2[p])||(o1[j]==o2[k]&&o1[i]==o2[p])){
 
									}
								}
							}
						}
					}
					int result=o1[0].compareTo(o2[0]);
					if(result==0)
					result=o1[1].compareTo(o2[1]);
					if(result==0)
					result=o1[2].compareTo(o2[2]);
					return result;
			}
		};
	}
	
	
	public static String reverseString(String s){
		StringBuilder input1 = new StringBuilder(); 
        input1.append(s);  
		input1 = input1.reverse();
		return input1.toString();
	}
	public static int[] scanArray(int n){
		int a[]=new int [n];
		for(int i=0;i<n;i++)
		a[i]=sc.nextInt();
 
		return a;
	}
	public static long[] scanLongArray(int n){
		long a[]=new long [n];
		for(int i=0;i<n;i++)
		a[i]=sc.nextLong();
 
		return a;
	}
	public static String [] scanStrings(int n){
		String a[]=new String [n];
		for(int i=0;i<n;i++)
		a[i]=sc.nextLine();
 
		return a;
	}
	static class InputReader {
 
		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;
 
		public InputReader(InputStream stream) {
			this.stream = stream;
		}
 
		public int snext() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
 
		public int nextInt() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextInt();
			}
			return a;
		}
 
		public String readString() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}
 
		public String nextLine() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isEndOfLine(c));
			return res.toString();
		}
 
		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
 
		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
 
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
 
}
class p{
	int a,b,c;
}
class SegmentTree{
	int s[],n, t;
	SegmentTree(int a[]){
		n=a.length;
		int l=(int)Math.ceil(Math.log(n)/Math.log(2));
		if(l%2==0)
		t=1;
		else
		t=0;
		l=2*(int)Math.pow(2,l)-1;
		s=new int[l];
		createSegmentTreeUtil(a, 0, 0, n-1,t);
	}
	
	int createSegmentTreeUtil(int a[],int root,int l,int r,int c){
		if(l==r)
		s[root]=a[l];
		else
		s[root]= Compare(createSegmentTreeUtil(a, 2*root+1, l, (l+r)/2,c^1), createSegmentTreeUtil(a,2*root+2, (l+r)/2+1,r,c^1),c);
		return s[root];
	}
	int getValue(){
		return s[0];
	}
	
	int update(int p,int k){
		return updateUtil(p, k,0,0,n-1,t);
	}
	int updateUtil(int p,int k,int root,int l,int r,int c){
		if(l==r&&l==k){
			s[root]=p;
			return s[root];
		}
		else if(l>k||r<k)
		return s[root];
		else{
			s[root]=Compare(updateUtil(p, k, 2*root+1, l, (l+r)/2,c^1), updateUtil(p, k, 2*root+2,(l+r)/2+1,r,c^1),c);
			return s[root];
		}
	}


	int Compare(int a,int b,int c){
		if(c==0)
		return a|b;
		else
		return a^b;
	}
}

class spair{
	String s1;
	String s2;
	spair(String r1,String r2){
		s1=r1;
		s2=r2;
	}
}
