Problem: Omkar has received a message from Anton saying "Your story for problem A is confusing. Just make a formal statement." Because of this, Omkar gives you an array a = [a_1, a_2, …, a_n] of n distinct integers. An array b = [b_1, b_2, …, b_k] is called nice if for any two distinct elements b_i, b_j of b, |b_i-b_j| appears in b at least once. In addition, all elements in b must be distinct. Can you add several (maybe, 0) integers to a to create a nice array b of size at most 300? If a is already nice, you don't have to add any elements.

For example, array [3, 6, 9] is nice, as |6-3|=|9-6| = 3, which appears in the array, and |9-3| = 6, which appears in the array, while array [4, 2, 0, 6, 9] is not nice, as |9-4| = 5 is not present in the array.

For integers x and y, |x-y| = x-y if x > y and |x-y| = y-x otherwise.

Input

Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 50), the number of test cases. Description of the test cases follows.

The first line of each test case contains a single integer n (2 ≤ n ≤ 100) — the length of the array a.

The second line of each test case contains n distinct integers a_1, a_2, ⋅⋅⋅, a_n (-100 ≤ a_i ≤ 100) — the elements of the array a.

Output

For each test case, output one line containing YES if Omkar can create a nice array b by adding elements to a and NO otherwise. The case of each letter does not matter, so yEs and nO will also be accepted.

If the first line is YES, output a second line containing a single integer k (n ≤ k ≤ 300). 

Then output one line containing k distinct integers b_1, b_2, ⋅⋅⋅, b_k (-10^9 ≤ b_i ≤ 10^9), the elements of the nice array b. b_1, b_2, ⋅⋅⋅, b_k can be in any order. For each a_i in a, a_i must appear at least once in b.

It can be proved that if Omkar can create such an array b, then he can also do so in a way that satisfies the above constraints.

If multiple solutions exist, you can print any. 

Example

Input


4
3
3 0 9
2
3 4
5
-7 3 13 -2 8
4
4 8 12 6


Output


yes
4
6 0 3 9
yEs
5
5 3 1 2 4
NO
Yes
6
8 12 6 2 4 10

Note

For the first case, you can add integers to a to receive the array b = [6, 0, 3, 9]. Note that |6-3| = |9-6| = |3-0| = 3 and 3 is in b, |6-0| = |9-3| = 6 and 6 is in b, and |9-0| = 9 is in b, so b is nice.

For the second case, you can add integers to a to receive the array b = [5, 3, 1, 2, 4]. We have that |2-1| = |3-2| = |4-3| = |5-4| = 1 is in b, |3-1| = |4-2| = |5-3| = 2 is in b, |4-1| = |5-2| = 3 is in b, and |5-1| = 4 is in b, so b is nice.

For the fourth case, you can add integers to a to receive the array b = [8, 12, 6, 2, 4, 10]. We have that |4-2| = |6-4| = |8-6| = |10-8| = |12-10| = 2 is in b, |6-2| = |8-4| = |10-6| = |12-8| = 4 is in b, |8-2| = |10-4| = |12-6| = 6 is in b, |10-2| = |12-4| = 8 is in b, and |12-2| = 10 is in b, so b is nice.

It can be proven that for all other test cases it is impossible to create a nice array b.

Solution (in JAVA):

Solution:


import java.io.*;
import java.util.*;

public class TestClass {

    public static class FastWriter {
        private static final int BUF_SIZE = 1 << 13;
        private final byte[] buf = new byte[BUF_SIZE];
        private final OutputStream out;
        private int ptr = 0;

        private FastWriter() {
            out = null;
        }

        public FastWriter(OutputStream os) {
            this.out = os;
        }

        public FastWriter(String path) {
            try {
                this.out = new FileOutputStream(path);
            } catch (FileNotFoundException e) {
                throw new RuntimeException("FastWriter");
            }
        }

        public FastWriter write(byte b) {
            buf[ptr++] = b;
            if (ptr == BUF_SIZE) innerflush();
            return this;
        }

        public FastWriter write(char c) {
            return write((byte) c);
        }

        public FastWriter write(char[] s) {
            for (char c : s) {
                buf[ptr++] = (byte) c;
                if (ptr == BUF_SIZE) innerflush();
            }
            return this;
        }

        public FastWriter write(String s) {
            s.chars().forEach(c -> {
                buf[ptr++] = (byte) c;
                if (ptr == BUF_SIZE) innerflush();
            });
            return this;
        }

        private static int countDigits(int l) {
            if (l >= 1000000000) return 10;
            if (l >= 100000000) return 9;
            if (l >= 10000000) return 8;
            if (l >= 1000000) return 7;
            if (l >= 100000) return 6;
            if (l >= 10000) return 5;
            if (l >= 1000) return 4;
            if (l >= 100) return 3;
            if (l >= 10) return 2;
            return 1;
        }

        public FastWriter write(int x) {
            if (x == Integer.MIN_VALUE) {
                return write((long) x);
            }
            if (ptr + 12 >= BUF_SIZE) innerflush();
            if (x < 0) {
                write((byte) '-');
                x = -x;
            }
            int d = countDigits(x);
            for (int i = ptr + d - 1; i >= ptr; i--) {
                buf[i] = (byte) ('0' + x % 10);
                x /= 10;
            }
            ptr += d;
            return this;
        }

        private static int countDigits(long l) {
            if (l >= 1000000000000000000L) return 19;
            if (l >= 100000000000000000L) return 18;
            if (l >= 10000000000000000L) return 17;
            if (l >= 1000000000000000L) return 16;
            if (l >= 100000000000000L) return 15;
            if (l >= 10000000000000L) return 14;
            if (l >= 1000000000000L) return 13;
            if (l >= 100000000000L) return 12;
            if (l >= 10000000000L) return 11;
            if (l >= 1000000000L) return 10;
            if (l >= 100000000L) return 9;
            if (l >= 10000000L) return 8;
            if (l >= 1000000L) return 7;
            if (l >= 100000L) return 6;
            if (l >= 10000L) return 5;
            if (l >= 1000L) return 4;
            if (l >= 100L) return 3;
            if (l >= 10L) return 2;
            return 1;
        }

        public FastWriter write(long x) {
            if (x == Long.MIN_VALUE) {
                return write("" + x);
            }
            if (ptr + 21 >= BUF_SIZE) innerflush();
            if (x < 0) {
                write((byte) '-');
                x = -x;
            }
            int d = countDigits(x);
            for (int i = ptr + d - 1; i >= ptr; i--) {
                buf[i] = (byte) ('0' + x % 10);
                x /= 10;
            }
            ptr += d;
            return this;
        }

        public FastWriter write(double x, int precision) {
            if (x < 0) {
                write('-');
                x = -x;
            }
            x += Math.pow(10, -precision) / 2;
            //		if(x < 0){ x = 0; }
            write((long) x).write(".");
            x -= (long) x;
            for (int i = 0; i < precision; i++) {
                x *= 10;
                write((char) ('0' + (int) x));
                x -= (int) x;
            }
            return this;
        }

        public FastWriter writeln(char c) {
            return write(c).writeln();
        }

        public FastWriter writeln(int x) {
            return write(x).writeln();
        }

        public FastWriter writeln(long x) {
            return write(x).writeln();
        }

        public FastWriter writeln(double x, int precision) {
            return write(x, precision).writeln();
        }

        public FastWriter write(int... xs) {
            boolean first = true;
            for (int x : xs) {
                if (!first) write(' ');
                first = false;
                write(x);
            }
            return this;
        }

        public FastWriter write(long... xs) {
            boolean first = true;
            for (long x : xs) {
                if (!first) write(' ');
                first = false;
                write(x);
            }
            return this;
        }

        public FastWriter writeln() {
            return write((byte) '\n');
        }

        public FastWriter writeln(int... xs) {
            return write(xs).writeln();
        }

        public FastWriter writeln(long... xs) {
            return write(xs).writeln();
        }

        public FastWriter writeln(char[] line) {
            return write(line).writeln();
        }

        public FastWriter writeln(char[]... map) {
            for (char[] line : map) write(line).writeln();
            return this;
        }

        public FastWriter writeln(String s) {
            return write(s).writeln();
        }

        private void innerflush() {
            try {
                out.write(buf, 0, ptr);
                ptr = 0;
            } catch (IOException e) {
                throw new RuntimeException("innerflush");
            }
        }

        public void flush() {
            innerflush();
            try {
                out.flush();
            } catch (IOException e) {
                throw new RuntimeException("flush");
            }
        }

        public FastWriter print(byte b) {
            return write(b);
        }

        public FastWriter print(char c) {
            return write(c);
        }

        public FastWriter print(char[] s) {
            return write(s);
        }

        public FastWriter print(String s) {
            return write(s);
        }

        public FastWriter print(int x) {
            return write(x);
        }

        public FastWriter print(long x) {
            return write(x);
        }

        public FastWriter print(double x, int precision) {
            return write(x, precision);
        }

        public FastWriter println(char c) {
            return writeln(c);
        }

        public FastWriter println(int x) {
            return writeln(x);
        }

        public FastWriter println(long x) {
            return writeln(x);
        }

        public FastWriter println(double x, int precision) {
            return writeln(x, precision);
        }

        public FastWriter print(int... xs) {
            return write(xs);
        }

        public FastWriter print(long... xs) {
            return write(xs);
        }

        public FastWriter println(int... xs) {
            return writeln(xs);
        }

        public FastWriter println(long... xs) {
            return writeln(xs);
        }

        public FastWriter println(char[] line) {
            return writeln(line);
        }

        public FastWriter println(char[]... map) {
            return writeln(map);
        }

        public FastWriter println(String s) {
            return writeln(s);
        }

        public FastWriter println() {
            return writeln();
        }
    }


    static final class InputReader {
        private final InputStream stream;
        private final byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int read() throws IOException {
            if (curChar >= numChars) {
                curChar = 0;
                numChars = stream.read(buf);
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public final int readInt() throws IOException {
            return (int) readLong();
        }

        public final long readLong() throws IOException {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
                if (c == -1) throw new IOException();
            }
            boolean negative = false;
            if (c == '-') {
                negative = true;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return negative ? -res : res;
        }

        public final int[] readIntArray(int size) throws IOException {
            int[] array = new int[size];
            for (int i = 0; i < size; i++) {
                array[i] = readInt();
            }
            return array;
        }

        public final long[] readLongArray(int size) throws IOException {
            long[] array = new long[size];
            for (int i = 0; i < size; i++) {
                array[i] = readLong();
            }
            return array;
        }

        public final String readString() throws IOException {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }

    static long mulmod(long a, long b,
                       long mod) {
        long res = 0; // Initialize result
        a = a % mod;
        while (b > 0) {
            // If b is odd, add 'a' to result
            if (b % 2 == 1) {
                res = (res + a) % mod;
            }

            // Multiply 'a' with 2
            a = (a * 2) % mod;

            // Divide b by 2
            b /= 2;
        }

        // Return result
        return res % mod;
    }

    static long pow(long a, long b, long MOD) {
        long x = 1, y = a;
        while (b > 0) {
            if (b % 2 == 1) {
                x = (x * y);
                if (x > MOD) x %= MOD;
            }
            y = (y * y);
            if (y > MOD) y %= MOD;
            b /= 2;
        }
        return x;
    }

    static long[] f = new long[200001];

    static long InverseEuler(long n, long MOD) {
        return pow(n, MOD - 2, MOD);
    }

    static long C(int n, int r, long MOD) {

        return (f[n] * ((InverseEuler(f[r], MOD) * InverseEuler(f[n - r], MOD)) % MOD)) % MOD;
    }


    static int[] h = {0, 0, -1, 1};
    static int[] v = {1, -1, 0, 0};


    public static class Pair {
        public int a;

        public int 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 == pair.a &&
                    b == pair.b;
        }

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

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

    static class Pair2 {
        public long cost;
        int node;

        public Pair2(long cos, int node) {
            this.cost = cos;
            this.node = node;
        }
    }

    static long compute_hash(String s) {
        int p = 31;
        int m = 1000000007;
        long hash_value = 0;
        long p_pow = 1;
        for (int i = 0; i < s.length(); ++i) {
            char c = s.charAt(i);
            hash_value = (hash_value + (c - 'a' + 1) * p_pow) % m;
            p_pow = (p_pow * p) % m;
        }
        return hash_value;
    }

    public static class SegmentTree {
        long[][] tree;
        int n;

        public SegmentTree(int[] nodes) {
            tree = new long[nodes.length * 4][2];
            n = nodes.length;
            build(0, n - 1, 0, nodes);

        }

        private void build(int l, int r, int pos, int[] nodes) {
            if (l == r) {
                tree[pos][0] = nodes[l];
                tree[pos][1] = l;
                return;
            }
            int mid = (l + r) / 2;
            build(l, mid, 2 * pos + 1, nodes);
            build(mid + 1, r, 2 * pos + 2, nodes);
            if (tree[2 * pos + 1][0] > tree[2 * pos + 2][0]) {
                tree[pos][1] = tree[2 * pos + 1][1];
            } else {
                tree[pos][1] = tree[2 * pos + 2][1];
            }
            tree[pos][0] = Math.max(tree[2 * pos + 1][0], tree[2 * pos + 2][0]);
        }

        //        public void update(int pos, int val) {
        //            updateUtil(0, n - 1, 0, pos, val);
        //        }

        public long[] get(int l, int r) {
            return getUtil(0, n - 1, 0, l, r);
        }

        private long[] getUtil(int l, int r, int pos, int ql, int qr) {
            if (ql > r || qr < l) {
                return new long[]{-1, -1};
            }
            if (l >= ql && r <= qr) {
                return tree[pos];
            }

            int mid = (l + r) / 2;
            long[] left = getUtil(l, mid, 2 * pos + 1, ql, qr);
            long[] right = getUtil(mid + 1, r, 2 * pos + 2, ql, qr);
            long choice = right[1];
            if (left[0] > right[0]) choice = left[1];
            return new long[]{Math.max(left[0], right[0]), choice};

        }

        //        private void updateUtil(int l, int r, int pos, int i, int val) {
        //            if (i < l || i > r) {
        //                return;
        //            }
        //            if (l == r) {
        //                tree[pos] = val;
        //                return;
        //            }
        //            int mid = (l + r) / 2;
        //            updateUtil(l, mid, 2 * pos + 1, i, val);
        //            updateUtil(mid + 1, r, 2 * pos + 2, i, val);
        //            tree[pos] = tree[2 * pos + 1] + tree[2 * pos + 2];
        //        }
    }

    static int counter = 0;
    static int[] rIn;
    static int[] rOut;
    static int[] lIn;
    static int[] lOut;
    private static int[] flatten;
    private static int[] lFlatten;
    static long answer = 0;

    static int VISITED = 1;
    static int VISITING = 2;

    static int[] DIRX = new int[]{0, 0, 1, -1};
    static int[] DIRY = new int[]{1, -1, 0, 0};

    public static class Pair22 {
        int num, pos;

        public Pair22(int x, int y) {
            this.num = x;
            this.pos = y;
        }
    }

    public static long sumofdig(long n) {
        long sum = 0;
        while (n > 0) {
            sum += n % 10;
            n /= 10;
        }
        return sum;
    }

    public static void main(String[] args) throws Exception {
        //https://i...content-available-to-author-only...e.com/ebRGa6
        InputReader in = new InputReader(System.in);

        FastWriter out = new FastWriter(System.out);


//
//        f[0] = 1;
//        f[1] = 1;
//        for (int i = 2; i < 200001; ++i) {
//            f[i] = f[i-1] * i;
//            f[i] %= 1000000007;
//        }
        int t = in.readInt();


        while (t-- > 0) {

            int n = in.readInt();

            Set<Integer> s = new HashSet<>();

            for (int i = 0; i < n; ++i) s.add(in.readInt());


            while (s.size() <= 301) {

                Integer[] cur = s.toArray(new Integer[0]);
                boolean found = false;
                for (int i = 0; i < cur.length && !found; ++i) {
                    for (int j = i + 1; j < cur.length; ++j) {
                        if (!s.contains(Math.abs(cur[i] - cur[j]))) {
                            s.add(Math.abs(cur[i] - cur[j]));
                            found = true;
                        }
                    }
                }
                if (!found) break;
            }

            if (s.size() <= 300) {

                System.out.println("YES");
                System.out.println(s.size());
                for (int x: s) {

                    System.out.print(x + " ");
                }

                System.out.println("");

            } else {

                System.out.println("NO");
            }





        }

    }

    private static void printBit(long maxBitSet, int m) {
        StringBuilder ans = new StringBuilder();

        while (maxBitSet > 0) {
            if (maxBitSet % 2 == 1) {
                ans.append("1");
            } else {
                ans.append("0");
            }
            maxBitSet /= 2;
        }

        for (int i = m - 1; i >= 0; --i) {
            if (i <= ans.length() - 1)
                System.out.print(ans.charAt(i));
            else
                System.out.print(0);
        }
        System.out.println();
    }

    private static void solvedd(int[] arr, int left, int right, int[] ans, int depth) {

        if (left > right) return;
        int maxInd = left;
        for (int i = left; i <= right; ++i) {
            if (arr[i] > arr[maxInd]) {
                maxInd = i;
            }
        }

        ans[maxInd] = depth;

        solvedd(arr, left, maxInd - 1, ans, depth + 1);
        solvedd(arr, maxInd + 1, right, ans, depth + 1);

    }


    private static void solved(List<List<Integer>> g, int node, int[][] dp, int last, int[] a) {

        int donttake = 0;
        int take = 0;
        for (int i = 0; i < g.get(node).size(); ++i) {
            int ntb = g.get(node).get(i);

            if (ntb != last) {
                solved(g, ntb, dp, node, a);
                donttake += Math.max(dp[ntb][0], dp[ntb][1]);
                take += dp[ntb][1];
            }
        }
        dp[node][0] = a[node] + take;
        dp[node][1] = donttake;
    }


    private static boolean solve(int n, List<Integer> nums, int cur, int pos, Boolean[][] dp) {
        if (cur > n) return false;
        if (cur == n) return true;
        if (pos >= nums.size()) return false;

        if (dp[cur][pos] != null) {
            return dp[cur][pos];
        }
        boolean without = solve(n, nums, cur, pos + 1, dp);
        boolean with = false;
        int ogcur = cur;
        for (int i = 1; i < 12; ++i) {
            with |= solve(n, nums, cur + nums.get(pos), pos + 1, dp);
            cur += nums.get(pos);
        }

        return dp[ogcur][pos] = with | without;
    }

//    private static Pair22 dfss(List<LinkedHashSet<Integer>> g, int node, HashSet<Integer> vis, int[] dis, int[] dis2) {
//        if (vis.contains(node)) return new Pair22(dis[node], dis2[node], -1);
//        vis.add(node);
//        int min = dis[node];
//        for (Integer ntb : g.get(node)) {
//            if (dis[ntb] > dis[node])
//                dfss(g, ntb, vis, dis, dis2);
//            if (dis[ntb] <= dis[node]) {
//                min = Math.min(min, dis[ntb]);
//            } else {
//                min = Math.min(min, dis2[ntb]);
//            }
//        }
//        //        if (dis)
//        dis2[node] = min;
//        return new Pair22(dis[node], min, -1);
//    }


    private static int dfs(HashMap<Pair, TreeSet<Pair>> grid, int x, int y, int ti, HashSet<Pair> vis, int r, int startX, int startY) {
        //        System.out.println(x + "  " + y);
        int taken = ti - Math.abs(startX - x) - Math.abs(startY - y);
        if (taken < 0) return 0;
        if (x < 0 || y < 0 || x > r || y > r) return 0;
        if (vis.contains(new Pair(x, y))) return 0;
        int max = 0;

        if (grid.containsKey(new Pair(x, y))) {
            TreeSet<Pair> times = grid.get(new Pair(x, y));
            for (Pair t : times) {
                if (t.a <= taken) {
                    max = Math.max(t.b, max);
                } else break;
            }
        }
        vis.add(new Pair(x, y));
        max = Math.max(dfs(grid, x + 1, y, ti, vis, r, startX, startY), max);
        max = Math.max(dfs(grid, x, y + 1, ti, vis, r, startX, startY), max);
        max = Math.max(dfs(grid, x - 1, y, ti, vis, r, startX, startY), max);
        max = Math.max(dfs(grid, x, y - 1, ti, vis, r, startX, startY), max);
        return max;
    }

    private static int solver(int[] nums, int pos, int[] dp) {
        if (pos >= nums.length) return 0;
        if (dp[pos] != Integer.MAX_VALUE) return dp[pos];
        int min = solver(nums, pos + 2, dp) + nums[pos];
        min = Math.min(solver(nums, pos + 3, dp) + nums[pos], min);
        if (pos + 1 < nums.length) min = Math.min(min, nums[pos] + nums[pos + 1] + solver(nums, pos + 3, dp));
        if (pos + 1 < nums.length) min = Math.min(min, nums[pos] + nums[pos + 1] + solver(nums, pos + 4, dp));

        //        System.out.println(pos + " " + min);
        return dp[pos] = min;
    }


    static int countFreq(String pattern, String text) {
        int m = pattern.length();
        int n = text.length();
        int res = 0;

        for (int i = 0; i <= n - m; i++) {
            int j;
            for (j = 0; j < m; j++) {
                if (text.charAt(i + j) != pattern.charAt(j)) {
                    break;
                }
            }
            if (j == m) {
                res++;
                j = 0;
            }
        }
        return res;
    }

    private static void dfsR(List<List<Integer>> g, int node, int[] v) {
        rIn[node] = counter;
        flatten[counter++] = v[node];

        for (int i = 0; i < g.get(node).size(); ++i) {
            dfsR(g, g.get(node).get(i), v);
        }

        rOut[node] = counter;
        flatten[counter++] = v[node] * -1;
    }

    private static void dfsL(List<List<Integer>> g, int node, int[] v) {
        lIn[node] = counter;
        lFlatten[counter++] = v[node];

        for (int i = 0; i < g.get(node).size(); ++i) {
            dfsL(g, g.get(node).get(i), v);
        }

        lOut[node] = counter;
        lFlatten[counter++] = v[node] * -1;

        TreeMap<String, Integer> map = new TreeMap<>();
    }


    private static void preprocess(int pos, int[][] pre, List<List<Integer>> tree, int[] traverse, int depth, int last, int[] tin, int[] tout) {
        tin[pos] = counter++;
        traverse[depth] = pos;

        for (int i = 0; depth - (1 << i) >= 0; ++i) {
            pre[pos][i] = traverse[depth - (1 << i)];
        }

        for (int i = 0; i < tree.get(pos).size(); ++i) {
            if (tree.get(pos).get(i) != last)
                preprocess(tree.get(pos).get(i), pre, tree, traverse, depth + 1, pos, tin, tout);
        }
        tout[pos] = counter++;
    }

    static long gcd(long a, long b) {

        while (b != 0) {
            long t = a;
            a = b;
            b = t % b;
        }
        return a;
    }


    static boolean submit = true;

    static void debug(String s) {
        if (!submit)
            System.out.println(s);
    }

    static void debug(int s) {
        LinkedHashSet<Integer> exist = new LinkedHashSet<>();
            /*

            4 2 3 _ 2 4 3 _
             */
    }




/**


 0 1 2 3 4 5 6 7 8 9 10

 1               1   1
 * Your ExamRoom object will be instantiated and called as such:
 * ExamRoom obj = new ExamRoom(N);
 * int param_1 = obj.seat();
 * obj.leave(p);
 */
}