Yelisey has an array a of n integers.

If a has length strictly greater than 1, then Yelisei can apply an operation called minimum extraction to it: 

  1. First, Yelisei finds the minimal number m in the array. If there are several identical minima, Yelisey can choose any of them. 
  2. Then the selected minimal element is removed from the array. After that, m is subtracted from each remaining element. 



Thus, after each operation, the length of the array is reduced by 1.

For example, if a = [1, 6, -4, -2, -4], then the minimum element in it is a_3 = -4, which means that after this operation the array will be equal to a=[1 {- (-4)}, 6 {- (-4)}, -2 {- (-4)}, -4 {- (-4)}] = [5, 10, 2, 0].

Since Yelisey likes big numbers, he wants the numbers in the array a to be as big as possible.

Formally speaking, he wants to make the minimum of the numbers in array a to be maximal possible (i.e. he want to maximize a minimum). To do this, Yelisey can apply the minimum extraction operation to the array as many times as he wants (possibly, zero). Note that the operation cannot be applied to an array of length 1.

Help him find what maximal value can the minimal element of the array have after applying several (possibly, zero) minimum extraction operations to the array.

Input

The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The next 2t lines contain descriptions of the test cases.

In the description of each test case, the first line contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the original length of the array a. The second line of the description lists n space-separated integers a_i (-10^9 ≤ a_i ≤ 10^9) — elements of the array a.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

Print t lines, each of them containing the answer to the corresponding test case. The answer to the test case is a single integer — the maximal possible minimum in a, which can be obtained by several applications of the described operation to it.

Example

Input


8
1
10
2
0 0
3
-1 2 0
4
2 10 1 7
2
2 3
5
3 2 -4 -2 0
2
-1 1
1
-2


Output


10
0
2
5
2
2
2
-2

Note

In the first example test case, the original length of the array n = 1. Therefore minimum extraction cannot be applied to it. Thus, the array remains unchanged and the answer is a_1 = 10.

In the second set of input data, the array will always consist only of zeros.

In the third set, the array will be changing as follows: [\color{blue}{-1}, 2, 0] → [3, \color{blue}{1}] → [\color{blue}{2}]. The minimum elements are highlighted with \color{blue}{blue}. The maximal one is 2.

In the fourth set, the array will be modified as [2, 10, \color{blue}{1}, 7] → [\color{blue}{1}, 9, 6] → [8, \color{blue}{5}] → [\color{blue}{3}]. Similarly, the maximum of the minimum elements is 5.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

import static java.lang.Math.log;
import static java.lang.Math.min;

public class Main {

    //------------------------------------------CONSTANTS---------------------------------------------------------------
    public static final int MOD = (int) (1e9 + 7);

    //---------------------------------------------I/0------------------------------------------------------------------

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(
                    new InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() { return Integer.parseInt(next()); }

        long nextLong() { return Long.parseLong(next()); }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static void print(String s) {
        System.out.println(s);
    }

    public static void main(String[] args) {
        FastReader sc = new FastReader();

        int t = 1;
        t = sc.nextInt();

        for(int i = 0; i<t; i++) {
            System.out.println(solve(sc));
        }
    }

    //------------------------------------------------SOLVE-------------------------------------------------------------

    public static long solve(FastReader sc) {
        int n = sc.nextInt(); int[] a = new int[n];
        for (int i = 0; i<n; i++) {
            a[i] = sc.nextInt();
        }
        if (n == 1)
            return a[0];

        OrderedMultiSet<Integer> set = new OrderedMultiSet<>();
        for (int i = 0; i<n; i++) {
            set.add(a[i]);
        }

        int toRemove = 0;
        int res = set.first();
        while (set.size() > 1) {
            toRemove += set.pollFirst()-toRemove;
            if (set.first() - toRemove > res) {
                res = set.first() - toRemove;
            }
        }
        res = Math.max(res, set.first() - toRemove);
        return res;
    }

    public static int firstNotDivisor(int n, int z) {
        for (int i = z; i>=1; i--) {
            if (n%i!=0)
                return i;
        }
        return -1;
    }

    public static int factorial(int n) {
        if (n == 0)
            return 1;
        int fact = 1;
        for (int i = 2; i<=n; i++) {
            fact *= i;
        }
        return fact;
    }

    public static int maxFactorial(int n) {
        int k = 1;
        int fact = 1;
        while ((k+1)*fact < n) {
            k++;
            fact *= k;
        }
        return k;
    }

    public static boolean isPalindrome(String s) {
        for (int i = 0; i<s.length()/2; i++) {
            if (s.charAt(i) != s.charAt(s.length()-1-i))
                return false;
        }
        return true;
    }

    //-----------------------------------------------FUNCTIONS----------------------------------------------------------

    public static String printArray(int[] a) {
        StringBuilder r = new StringBuilder("");

        for(int i = 0; i<a.length; i++) {
            r.append(a[i] + " ");
        }
        return r.toString();
    }

    public static <T> String printList(List<T> a) {
        StringBuilder r = new StringBuilder("");

        for (T x: a) {
            r.append(x.toString() + " ");
        }
        return r.toString();
    }

    // first element that is not less than target
    public static int lowerBound(int[] arr, int begin, int end, int target) {
        while(begin < end) {
            int mid = begin + (end - begin) / 2;
            // When the element is less than the mid target
            if(arr[mid] < target)
                // begin to mid + 1, arr [begin] value is less than or equal target
                begin = mid + 1;
                // When the mid target element when greater than or equal
            else if(arr[mid] >= target)
                end = mid;
        }
        return begin;
    }

    // first element that is greater than target
    public static int upperBound(int[] arr, int begin, int end, int target) {
        while(begin < end) {
            int mid = begin + (end - begin) / 2;
            if(arr[mid] <= target)
                begin = mid + 1;
            else
                end = mid;
        }
        return begin;
    }

    // generate permutations (call search and access through permutations)
    public static class Permutations {
        List<List<Integer>> permutations = new ArrayList<>();
        List<Integer> permutation = new ArrayList<>();
        boolean[] taken;
        int[] a;

        public Permutations(int[] a) {
            this.a = a;
            taken = new boolean[a.length];
        }

        void search() {
            if (permutation.size()==a.length) {
                permutations.add(new ArrayList<>(permutation));
            } else {
                for (int i = 0; i<a.length; i++) {
                    if (taken[i]) {
                        continue;
                    }
                    taken[i] = true;
                    permutation.add(a[i]);
                    search();
                    taken[i] = false;
                    permutation.remove(permutation.size()-1);
                }
            }
        }
    }

    // generate subsets (call search and access subsets)
    public static class Subsets {
        List<List<Integer>> subsets = new ArrayList<>();
        List<Integer> subset = new ArrayList<>();

        void search(int[] a, int x) {
            if (x == a.length) {
                subsets.add(new ArrayList<>(subset));
            } else {
                subset.add(a[x]);
                search(a, x+1);
                subset.remove(subset.size() - 1);
                search(a, x+1);
            }
        }
    }

    public static int gcd(int a, int b) {
        while (b != 0) {
            int t = b;
            b = a % b;
            a = t;
        }
        return a;
    }

    public static int lcm(int a, int b) {
        return (a*b)/gcd(a, b);
    }

    public static int[] prefixSum(int[] a) {
        int n = a.length;
        int[] ps = new int[n];
        ps[0] = a[0];

        for (int i = 1; i<n; i++) {
            ps[i] = ps[i-1] + a[i];
        }

        return ps;
    }

    public static int[][] prefixSum2D(int[][] a) {
        int n = a.length;
        int m = a[0].length;
        int[][] ps = new int[n][m];
        ps[0][0] = a[0][0];

        for (int j = 1; j<m; j++) {
            ps[0][j] = ps[0][j-1] + a[0][j];
        }
        for (int i = 1; i<n; i++) {
            ps[i][0] = ps[i-1][0] + a[i][0];
        }

        for (int i = 1; i<n; i++) {
            for (int j = 1; j<m; j++) {
                ps[i][j] = ps[i-1][j] + ps[i][j-1] - ps[i-1][j-1] + a[i][j];
            }
        }

        return ps;
    }

    public static double log2(double a) {
        return log(a)/log(2);
    }

    //----------------------------------------DATA-STRUCTURES-----------------------------------------------------------

    // Range queries (i.e. RMQ) in O(1), others with functions in O(log n)
    public static class SparseTable {
        int[][] st;
        int n;
        int k;

        public SparseTable(int[] a) {
            n = a.length;
            k = (int) log2(n);
            st = new int[n][k+1];

            for (int i = 0; i<n; i++) {
                st[i][0] = a[i];
            }

            // 1<<j == 2^j
            for (int j = 1; j<=k; j++) {
                for (int i = 0; i + (1 << j) <= n; i++) {
                    st[i][j] = min(st[i][j-1], st[i + (1 << (j - 1))][j - 1]);
                }
            }
        }

        //not always available O(log n) -- change the constructor to use it
        public long sumQuery(int l, int r) {
            long sum = 0;
            for (int j = k; j>=0; j--) {
                if ((1 << j) <= r - l + 1) {
                    sum += st[l][j];
                    l += 1 << j;
                }
            }

            return sum;
        }

        //always available O(1) -- change this and the constructor for rangeMaxQuery
        public int rangeMinQuery(int l, int r) {
            int j = (int) log2(r - l + 1);
            int min = min(st[l][j], st[r - (1 << j) + 1][j]);
            return min;
        }

    }

    //Range Sum Dynamic Queries O(log n)
    public static class BinaryIndexedTree {

        int[] bit;

        public BinaryIndexedTree(int[] a) {
            int n = a.length;
            bit = new int[n+1];
            // Store the actual values in BITree[]
            // using update()
            for(int i = 0; i < n; i++)
                updateBit(i, a[i]);
        }

        // O(log n) update delta at index in the array (do it on the array and then call this function)
        public void updateBit(int index, int delta) {
            index += 1;

            while (index <= bit.length) {
                bit[index] += delta;

                index += index & (-index);
            }
        }

        // Computes sum a[0...index] in O(log n)
        public int getSum(int index) {
            int sum = 0;

            index += 1;

            while (index > 0) {
                sum += bit[index];

                index -= index & (-index);
            }

            return sum;
        }
    }

    public static class UnionFind {

        int[] link;
        int[] size;

        UnionFind(int n) {
            link = new int[n];
            size = new int[n];
            for (int i = 0; i<n; i++) {
                link[i] = i;
                size[i] = 1;
            }
        }

        int find(int x) {
            while (x != link[x]) x = link[x];
            return x;
        }

        boolean same(int a, int b) {
            return find(a) == find(b);
        }

        void unite(int a, int b) {
            a = find(a);
            b = find(b);

            if (size[a] < size[b]) {
                int temp = a;
                a = b;
                b = temp;
            }

            size[a] += size[b];
            link[b] = a;
        }
    }

    public static class SegmentTree {

        int st[];

        public SegmentTree(int arr[]) {
            int n = arr.length;

            int x = (int) (Math.ceil(log2(n)));

            int maxSize = 2 * (int) Math.pow(2, x) - 1;

            st = new int[maxSize];

            build(arr, 0, n-1, 0);
        }

        int build(int arr[], int ss, int se, int si) {
            if (ss == se) {
                st[si] = arr[ss];
                return arr[ss];
            }

            int mid = ss + (se - ss) / 2; //ss+se/2

            st[si] = build(arr, ss, mid, si * 2 + 1) +
                    build(arr, mid + 1, se, si * 2 + 2);
            return st[si];
        }

        private int getSumUtil(int ss, int se, int l, int r, int si) {
            if (l <= ss && r >= se) {
                return st[si];
            }

            if (se < l || ss > r) {
                return 0;
            }

            int mid = ss + (se - ss) / 2;
            return getSumUtil(ss, mid, l, r, 2 * si + 1) +
                    getSumUtil(mid + 1, se, l, r, 2 * si + 2);
        }

        void updateValueUtil(int ss, int se, int i, int diff, int si) {
            if (i < ss || i > se) {
                return;
            }

            st[si] = st[si] + diff;
            if (se != ss) {
                int mid = ss + (se - ss) / 2;
                updateValueUtil(ss, mid, i, diff, 2 * si + 1);
                updateValueUtil(mid + 1, se, i, diff, 2 * si + 2);
            }
        }

        int getSum(int n, int l, int r) {
            if (l < 0 || r > n - 1 || l > r) {
                return -1;
            }

            return getSumUtil(0, n-1, l, r, 0);
        }

        // don't do it directly on the array but use this function that will
        // do everything for you
        void updateValue(int arr[], int n, int i, int newValue) {
            if (i < 0 || i > n - 1) {
                return;
            }

            int diff = newValue - arr[i];

            arr[i] = newValue;

            updateValueUtil(0, n - 1, i, diff, 0);
        }
    }

    // Similar to Pair in c++, non-null objects as parameters
    public static class Pair<T extends Comparable<T>, Q extends Comparable<Q>> implements Comparable<Pair<T, Q>>{
        T a;
        Q b;

        public Pair(T a, Q b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair<?, ?> pair = (Pair<?, ?>) o;
            return a.equals(pair.a) && b.equals(pair.b);
        }

        @Override
        public int hashCode() {
            return Objects.hash(a, b);
        }


        @Override
        public int compareTo(Pair<T, Q> tqPair) {
            int compareA = this.a.compareTo(tqPair.a);

            if (compareA == 0) {
                return this.b.compareTo(tqPair.b);
            } else {
                return compareA;
            }
        }
    }

    // Uses Map + TreeSet to get the structure
    public static class OrderedMultiSet<T extends Comparable<T>> {
        private final TreeSet<T> set = new TreeSet<>();
        private final Map<T, Integer> frequencies = new HashMap<>();
        private int size = 0;

        public OrderedMultiSet() {}

        public OrderedMultiSet(List<T> a) {
            for (T x: a) {
                this.add(x);
                size++;
            }
        }

        public void add(T element) {
            set.add(element);
            if (!frequencies.containsKey(element)) {
                frequencies.put(element, 0);
            }
            frequencies.put(element, frequencies.get(element) + 1);
            size++;
        }

        public boolean remove(T element) {
            if (frequencies.containsKey(element)) {
                int x = frequencies.get(element);
                x--;
                if (x == 0) {
                    frequencies.remove(element);
                    set.remove(element);
                } else {
                    frequencies.put(element, frequencies.get(element) - 1);
                }
                size--;
                return true;
            }
            return false;
        }

        public int size() {
            return size;
        }

        public T first() {
            return set.first();
        }

        public T last() {
            return set.last();
        }

        public T pollFirst() {
            T t = set.first();
            remove(t);
            return t;
        }

        public T pollLast() {
            T t = set.last();
            set.
            remove(t);
            return t;
        }
    }
}