Problem: One Saturday afternoon Egor was playing his favorite RPG game. While discovering new lands and territories, he came across the following sign:

<image>

Egor is a passionate player, but he is an algorithmician as well. That's why he instantly spotted four common letters in two words on the sign above — if we permute the letters "R", "E", "G", "O" from the first word, we can obtain the letters "O", "G", "R", "E". Egor got inspired by the sign and right away he came up with a problem about permutations.

You are given a permutation of length n. You have to split it into some non-empty subsequences so that each element of the permutation belongs to exactly one subsequence. Each subsequence must be monotonic — that is, either increasing or decreasing.

Sequence is called to be a subsequence if it can be derived from permutation by deleting some (possibly none) elements without changing the order of the remaining elements.

The number of subsequences should be small enough — let f(n) be the minimum integer k such that every permutation of length n can be partitioned into at most k monotonic subsequences.

You need to split the permutation into at most f(n) monotonic subsequences.

Input

The first line contains one integer t (1 ≤ t ≤ 10^5) — the number of test cases.

You can only use t = 1 in hacks.

Next, descriptions of t test cases come, each of them in the following format.

The first line of a single test case contains one integer n (1 ≤ n ≤ 10^5) — the length of the permutation. The second line contains n distinct integers a_i (1 ≤ a_i ≤ n) — the permutation itself.

The sum of the values of n over all test cases doesn't exceed 10^5.

Output

For each test case print the answer in the following format:

In the first line print k (1 ≤ k ≤ f(n)) — the number of the subsequences in the partition. In the next k lines, print the descriptions of found subsequences. Each description should start with a number l_i (1 ≤ l_i ≤ n) — the length of the corresponding subsequence, followed by l_i integers — the values of this subsequence in the order in which they occur in the permutation.

Each subsequence you output must be either increasing or decreasing. 

In case there are multiple possible answers, print any of them.

Example

Input


3
4
4 3 1 2
6
4 5 6 1 3 2
10
1 2 3 4 5 6 7 8 9 10


Output


2
3 4 3 1
1 2
3
2 4 1
2 5 6
2 3 2
1
10 1 2 3 4 5 6 7 8 9 10

Note

In the example, we can split:

  * [4, 3, 1, 2] into [4, 3, 1], [2] 
  * [4, 5, 6, 1, 3, 2] into [4, 1], [5, 6] and [3, 2] 
  * [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] into [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] 



Surely, there are many more answers possible.

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.*;
import java.util.*;
import java.util.stream.*;

public class E {

	int f(int n) {
		int ret = 0;
		while (n >= 0) {
			ret++;
			n -= ret;
		}
		return ret - 1;
	}

	void solve(int[] p) {
		int n = p.length;

		int[] tmp = new int[n + 1];
		boolean[] dead = new boolean[n];
		int live = n;

		int[] prv = new int[n];

		ArrayList<ArrayList<Integer>> ret = new ArrayList<>();

		int okMax = f(n);

		int[] color = new int[n];
		
		while (live > 0) {
			int size = 0;
			for (int i = 0; i < n; i++) {
				if (dead[i]) {
					continue;
				}
				int valHere = p[i];
				int low = -1, high = size;
				while (high - low > 1) {
					int mid = (low + high) >> 1;
					int valMid = p[tmp[mid]];
					if (valHere < valMid) {
						high = mid;
					} else {
						low = mid;
					}
				}
				color[i] = high;
				prv[i] = high == 0 ? -1 : tmp[high - 1];
				tmp[high] = i;
				if (high == size) {
					size++;
				}
			}
			// s0 = size;
			// last0 = tmp[size - 1];
			if (size <= okMax) {
				ArrayList<Integer>[] shit = new ArrayList[size];
				for (int i = 0; i < size; i++) {
					shit[i] = new ArrayList<>();
				}
				for (int i = 0; i < n; i++) {
					if (!dead[i]) {
						shit[color[i]].add(i);
					}
				}
				for (ArrayList<Integer> al : shit) {
					ret.add(al);
				}
				// blah-blah
				break;
			} else {

				ArrayList<Integer> arr = new ArrayList<>(size);

				live -= size;

				for (int i = tmp[size - 1], j = size - 1; j >= 0; j--) {
//					arr[j] = i;
					arr.add(i);
					dead[i] = true;
					i = prv[i];
				}
				
				Collections.reverse(arr);

				ret.add(arr);
				okMax--;
			}
		}

		out.println(ret.size());
		for (ArrayList<Integer> arr : ret) {
			out.println(arr.size());
			for (int idx : arr) {
				out.print((p[idx] + 1) + " ");
			}
			out.println();
		}
	}

	void submit() {
		int t = nextInt();
		while (t-- > 0) {
			int n = nextInt();
			int[] p = new int[n];
			for (int i = 0; i < n; i++) {
				p[i] = nextInt() - 1;
			}
			solve(p);
		}
	}

	void test() {
		// int[] dp = new int[100000];
		// for (int i = 1; i < dp.length; i++) {
		// dp[i] = dp[i - sq(i)] + 1;
		// System.err.println(i + " " + dp[i]);
		// }
	}

	void stress() {
		for (int tst = 0;; tst++) {
			if (false) {
				throw new AssertionError();
			}
			System.err.println(tst);
		}
	}

	E() throws IOException {
		is = System.in;
		out = new PrintWriter(System.out);
		submit();
		// stress();
		// test();
		out.close();
	}

	static final Random rng = new Random();
	static final int C = 5;

	static int rand(int l, int r) {
		return l + rng.nextInt(r - l + 1);
	}

	public static void main(String[] args) throws IOException {
		new E();
	}

	private InputStream is;
	PrintWriter out;

	private byte[] buf = new byte[1 << 14];
	private int bufSz = 0, bufPtr = 0;

	private int readByte() {
		if (bufSz == -1)
			throw new RuntimeException("Reading past EOF");
		if (bufPtr >= bufSz) {
			bufPtr = 0;
			try {
				bufSz = is.read(buf);
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
			if (bufSz <= 0)
				return -1;
		}
		return buf[bufPtr++];
	}

	private boolean isTrash(int c) {
		return c < 33 || c > 126;
	}

	private int skip() {
		int b;
		while ((b = readByte()) != -1 && isTrash(b))
			;
		return b;
	}

	String nextToken() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!isTrash(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	String nextString() {
		int b = readByte();
		StringBuilder sb = new StringBuilder();
		while (!isTrash(b) || b == ' ') {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

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

	char nextChar() {
		return (char) skip();
	}

	int nextInt() {
		int ret = 0;
		int b = skip();
		if (b != '-' && (b < '0' || b > '9')) {
			throw new InputMismatchException();
		}
		boolean neg = false;
		if (b == '-') {
			neg = true;
			b = readByte();
		}
		while (true) {
			if (b >= '0' && b <= '9') {
				ret = ret * 10 + (b - '0');
			} else {
				if (b != -1 && !isTrash(b)) {
					throw new InputMismatchException();
				}
				return neg ? -ret : ret;
			}
			b = readByte();
		}
	}

	long nextLong() {
		long ret = 0;
		int b = skip();
		if (b != '-' && (b < '0' || b > '9')) {
			throw new InputMismatchException();
		}
		boolean neg = false;
		if (b == '-') {
			neg = true;
			b = readByte();
		}
		while (true) {
			if (b >= '0' && b <= '9') {
				ret = ret * 10 + (b - '0');
			} else {
				if (b != -1 && !isTrash(b)) {
					throw new InputMismatchException();
				}
				return neg ? -ret : ret;
			}
			b = readByte();
		}
	}
}