The sequence of m integers is called the permutation if it contains all integers from 1 to m exactly once. The number m is called the length of the permutation.

Dreamoon has two permutations p_1 and p_2 of non-zero lengths l_1 and l_2.

Now Dreamoon concatenates these two permutations into another sequence a of length l_1 + l_2. First l_1 elements of a is the permutation p_1 and next l_2 elements of a is the permutation p_2. 

You are given the sequence a, and you need to find two permutations p_1 and p_2. If there are several possible ways to restore them, you should find all of them. (Note that it is also possible that there will be no ways.)

Input

The first line contains an integer t (1 ≤ t ≤ 10 000) denoting the number of test cases in the input.

Each test case contains two lines. The first line contains one integer n (2 ≤ n ≤ 200 000): the length of a. The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ n-1).

The total sum of n is less than 200 000.

Output

For each test case, the first line of output should contain one integer k: the number of ways to divide a into permutations p_1 and p_2.

Each of the next k lines should contain two integers l_1 and l_2 (1 ≤ l_1, l_2 ≤ n, l_1 + l_2 = n), denoting, that it is possible to divide a into two permutations of length l_1 and l_2 (p_1 is the first l_1 elements of a, and p_2 is the last l_2 elements of a). You can print solutions in any order.

Example

Input


6
5
1 4 3 2 1
6
2 4 1 3 2 1
4
2 1 1 3
4
1 3 3 1
12
2 1 3 4 5 6 7 8 9 1 10 2
3
1 1 1


Output


2
1 4
4 1
1
4 2
0
0
1
2 10
0

Note

In the first example, two possible ways to divide a into permutations are \{1\} + \{4, 3, 2, 1\} and \{1,4,3,2\} + \{1\}.

In the second example, the only way to divide a into permutations is \{2,4,1,3\} + \{2,1\}.

In the third example, there are no possible ways.
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;
 
public class Main {
	static final int INF = (int) (1e9 + 10);
	static final int MOD = (int) (1e9 + 7);
 
	// static final int N = (int) (4e5 + 5);
	// static ArrayList<Integer>[] graph;
	// static boolean visited[];
	// static long size[];
 
	public static void main(String[] args) throws NumberFormatException, IOException {
		FastReader sc = new FastReader();
		PrintWriter pr = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
		  //  int x = sc.nextInt();
		    int [] arr = new int[n];
		    long sum =0;
		  
		    for(int i =0 ; i < n; i++){
		        arr[i] = sc.nextInt();
		      //  ts.add(arr[i]);
		        sum += arr[i];
		    }
		    TreeSet<Integer> set = new TreeSet<>();
		     TreeSet<Integer> ps = new TreeSet<>();
		     TreeSet<Integer> ss = new TreeSet<>();
            ArrayList<Integer> ans = new ArrayList<>();
            long curr =0;
            for(int i =0 ; i < n ; i++){
                if(ps.contains(arr[i])){
                    break;
                }
                ps.add(arr[i]);
                if(ps.last() == (i+1)){
                    set.add(i+1);
                }
            }
            for(int i =n-1 ; i >= 0 ; i-- ){
                if(ss.contains(arr[i])){
                    break;
                }
                ss.add(arr[i]);
                if(ss.last() == (n-i) && set.contains(i)){
                    // ans.add(s s.last());
                    ans.add(i);
                }
            }
            pr.println(ans.size());
            for(int a : ans){
                pr.println(a + " "+  (n-a));
            }
            
            
            
            
            
            
            
            
            
		}
		
	
		
		pr.flush();
		pr.close();
	}
 
	/*
	 * Template From Here
	 */
	
	public static int lowerBound(ArrayList<Integer> array, int length, long value) {
		int low = 0;
		int high = length;
		while (low < high) {
			final int mid = (low + high) / 2;
			if (value <= array.get(mid)) {
				high = mid;
			} else {
				low = mid + 1;
			}
		}
		return low;
	}
 
	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;
		}
	}
 
	static long gcd(long a, long b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}
 
	static long lcm(long a, long b) {
		return (a * b) / gcd(a, b);
	}
 
	public static void sortbyColumn(int[][] att, int col) {
		// Using built-in sort function Arrays.sort
		Arrays.sort(att, new Comparator<int[]>() {
 
			@Override
			// Compare values according to columns
			public int compare(final int[] entry1, final int[] entry2) {
 
				// To sort in descending order revert
				// the '>' Operator
				// if (entry1[col] > entry2[col])
				// return 1;
				// else //(entry1[col] >= entry2[col])
				// return -1;
				return new Integer(entry1[col]).compareTo(entry2[col]);
				// return entry1[col].
			}
		}); // End of function call sort().
	}
 
	static class pair {
		int V, I;
 
		pair(int v, int i) {
			V = v;
			I = i;
		}
	}
 
	public static int[] swap(int data[], int left, int right) {
		int temp = data[left];
		data[left] = data[right];
		data[right] = temp;
		return data;
	}
 
	public static int[] reverse(int data[], int left, int right) {
		while (left < right) {
			int temp = data[left];
			data[left++] = data[right];
			data[right--] = temp;
		}
		return data;
	}
 
	public static boolean findNextPermutation(int data[]) {
		if (data.length <= 1)
			return false;
 
		int last = data.length - 2;
		while (last >= 0) {
			if (data[last] < data[last + 1]) {
				break;
			}
			last--;
		}
		if (last < 0)
			return false;
 
		int nextGreater = data.length - 1;
		for (int i = data.length - 1; i > last; i--) {
			if (data[i] > data[last]) {
				nextGreater = i;
				break;
			}
		}
		data = swap(data, nextGreater, last);
		data = reverse(data, last + 1, data.length - 1);
		return true;
	}
 
	static long nCr(long n, long r) {
		if (n == r)
			return 1;
		return fact(n) / (fact(r) * fact(n - r));
	}
 
	static long fact(long n) {
		long res = 1;
		for (long i = 2; i <= n; i++)
			res = res * i;
		return res;
	}
 
	/*
	 * static boolean prime[] = new boolean[1000007];
	 * 
	 * public static void sieveOfEratosthenes(int n) {
	 * 
	 * for (int i = 0; i < n; i++) prime[i] = true; * for (int p = 2; p * p <=
	 * n; p++) { // If prime[p] is not changed, then it is a prime if (prime[p]
	 * == true) { // Update all multiples of p for (int i = p * p; i <= n; i +=
	 * p) prime[i] = false; } }
	 * 
	 * // Print all prime numbers // for(int i = 2; i <= n; i++) // { //
	 * if(prime[i] == true) // System.out.print(i + " "); // } }
	 */
 
	static long power(long fac2, int y, int p) {
		long res = 1;
		fac2 = fac2 % p;
		while (y > 0) {
			if (y % 2 == 1)
				res = (res * fac2) % p;
			fac2 = (fac2 * fac2) % p;
		}
		return res;
	}
 
	static long modInverse(long fac2, int p) {
		return power(fac2, p - 2, p);
	}
 
	static boolean isPrime(int n) {
		// Corner cases
		if (n <= 1)
			return false;
		if (n <= 3)
			return true;
 
		// This is checked so that we can skip
		// middle five numbers in below loop
		if (n % 2 == 0 || n % 3 == 0)
			return false;
 
		for (int i = 5; i * i <= n; i = i + 6)
			if (n % i == 0 || n % (i + 2) == 0)
				return false;
 
		return true;
	}
 
	public static BigInteger lcmm(String a, String b) {
		BigInteger s = new BigInteger(a);
		BigInteger s1 = new BigInteger(b);
		BigInteger mul = s.multiply(s1);
		BigInteger gcd = s.gcd(s1);
		BigInteger lcm = mul.divide(gcd);
		return lcm;
	}
 
}