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.math.*;
import java.io.*;
import java.util.*;
import java.awt.*;
public class Solution {
    static Helper hp;
    final static int MAXN = 1000_006;
    final static long MOD = (long) 1e9 + 7;
    public static void main(String []args)throws Exception
    {
        hp=new Helper(MOD,MAXN);
        //hp.initIO("input.txt","output.txt");
        hp.initIO(System.in,System.out);
        solve();
    }
    static void solve()throws Exception{
        boolean testCases = true;
   	    int tc = testCases ? hp.nextInt() : 1;
        for (int tce = 1; tce <= tc; tce++) {
        		int n=hp.nextInt();
        		int a[]=hp.getIntArray(n);
        		HashSet<Integer> set=new HashSet<>();
        		HashSet<Integer> set1=new HashSet<>();
        		int max=0,max1=0;
        		boolean p[]=new boolean[n];
        		boolean p1[]=new boolean[n];
        		for(int i=0;i<n;i++)
        		{
        			if(set.contains(a[i]))
        			{
        				//index=i;
        				break;
        			}
        			set.add(a[i]);
        			max=hp.max(a[i],max);
        			if(set.size()==max)
        				p[i]=true;
        		}
        		for(int i=n-1;i>=0;i--)
        		{
        			if(set1.contains(a[i]))
        			{
        				//index=i;
        				break;
        			}
        			set1.add(a[i]);
        			max1=hp.max(a[i],max1);
        			if(set1.size()==max1)
        				p1[i]=true;
        		}
        		//hp.println(Arrays.toString(p));
        		//hp.println(Arrays.toString(p1));
        		int count=0;
        		StringBuilder sb=new StringBuilder();
        		for(int i=0;i<n-1;i++)
        		{
        			if(p[i] && p1[i+1])
        			{
        				count++;
        				sb.append((i+1)+" "+(n-i-1)+"\n");
        			}
        		}
        		hp.println(count);
        		hp.print(sb);

        }
        hp.flush();
    }

}

class Helper {
    final long MOD;
    final int MAXN;
    final Random rnd;

    public Helper(long mod, int maxn) {
        MOD = mod;
        MAXN = maxn;
        rnd = new Random();
    }


    public static int[] sieve;
    public static ArrayList<Integer> primes;

    public void setSieve() {
        primes = new ArrayList<>();
        sieve = new int[MAXN];
        int i, j;
        for (i = 2; i < MAXN; ++i)
            if (sieve[i] == 0) {
                primes.add(i);
                for (j = i; j < MAXN; j += i) {
                    sieve[j] = i;
                }
            }
    }


    public static long[] factorial;

    public void setFactorial() {
        factorial = new long[MAXN];
        factorial[0] = 1;
        for (int i = 1; i < MAXN; ++i) factorial[i] = factorial[i - 1] * i % MOD;
    }

    public long getFactorial(int n) {
        if (factorial == null) setFactorial();
        return factorial[n];
    }

    public long ncr(int n, int r) {
        if (r > n) return 0;
        if (factorial == null) setFactorial();
        long numerator = factorial[n];
        long denominator = factorial[r] * factorial[n - r] % MOD;
        return numerator * pow(denominator, MOD - 2, MOD) % MOD;
    }


    public long[] getLongArray(int size) throws Exception {
        long[] ar = new long[size];
        for (int i = 0; i < size; ++i) ar[i] = nextLong();
        return ar;
    }

    public int[] getIntArray(int size) throws Exception {
        int[] ar = new int[size];
        for (int i = 0; i < size; ++i) ar[i] = nextInt();
        return ar;
    }

    public String[] getStringArray(int size) throws Exception {
        String[] ar = new String[size];
        for (int i = 0; i < size; ++i) ar[i] = next();
        return ar;
    }

    public String joinElements(long... ar) {
        StringBuilder sb = new StringBuilder();
        for (long itr : ar) sb.append(itr).append(" ");
        return sb.toString().trim();
    }


    public String joinElements(int... ar) {
        StringBuilder sb = new StringBuilder();
        for (int itr : ar) sb.append(itr).append(" ");
        return sb.toString().trim();
    }

    public String joinElements(String... ar) {
        StringBuilder sb = new StringBuilder();
        for (String itr : ar) sb.append(itr).append(" ");
        return sb.toString().trim();
    }

    public String joinElements(Object... ar) {
        StringBuilder sb = new StringBuilder();
        for (Object itr : ar) sb.append(itr).append(" ");
        return sb.toString().trim();
    }


    public long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    public int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }


    public long max(long... ar) {
        long ret = ar[0];
        for (long itr : ar) ret = Math.max(ret, itr);
        return ret;
    }

    public int max(int... ar) {
        int ret = ar[0];
        for (int itr : ar) ret = Math.max(ret, itr);
        return ret;
    }

    public long min(long... ar) {
        long ret = ar[0];
        for (long itr : ar) ret = Math.min(ret, itr);
        return ret;
    }

    public int min(int... ar) {
        int ret = ar[0];
        for (int itr : ar) ret = Math.min(ret, itr);
        return ret;
    }


    public long sum(long... ar) {
        long sum = 0;
        for (long itr : ar) sum += itr;
        return sum;
    }

    public long sum(int... ar) {
        long sum = 0;
        for (int itr : ar) sum += itr;
        return sum;
    }

    public long pow(long base, long exp, long MOD) {
        base %= MOD;
        long ret = 1;
        while (exp > 0) {
            if ((exp & 1) == 1) ret = ret * base % MOD;
            base = base * base % MOD;
            exp >>= 1;
        }
        return ret;
    }


    static final int BUFSIZE = 1 << 20;
    static byte[] buf;
    static int index, total;
    static InputStream in;
    static BufferedWriter bw;


    public void initIO(InputStream is, OutputStream os) {
        try {
            in = is;
            bw = new BufferedWriter(new OutputStreamWriter(os));
            buf = new byte[BUFSIZE];
        } catch (Exception e) {
        }
    }

    public void initIO(String inputFile, String outputFile) {
        try {
            in = new FileInputStream(inputFile);
            bw = new BufferedWriter(new OutputStreamWriter(
                    new FileOutputStream(outputFile)));
            buf = new byte[BUFSIZE];
        } catch (Exception e) {
        }
    }

    private int scan() throws Exception {
        if (index >= total) {
            index = 0;
            total = in.read(buf);
            if (total <= 0)
                return -1;
        }
        return buf[index++];
    }

    public String next() throws Exception {
        int c;
        for (c = scan(); c <= 32; c = scan()) ;
        StringBuilder sb = new StringBuilder();
        for (; c > 32; c = scan())
            sb.append((char) c);
        return sb.toString();
    }

    public int nextInt() throws Exception {
        int c, val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+')
            c = scan();
        for (; c >= '0' && c <= '9'; c = scan())
            val = (val << 3) + (val << 1) + (c & 15);
        return neg ? -val : val;
    }

    public long nextLong() throws Exception {
        int c;
        long val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+')
            c = scan();
        for (; c >= '0' && c <= '9'; c = scan())
            val = (val << 3) + (val << 1) + (c & 15);
        return neg ? -val : val;
    }

    public void print(Object a) throws Exception {
        bw.write(a.toString());
    }

    public void printsp(Object a) throws Exception {
        print(a);
        print(" ");
    }

    public void println() throws Exception {
        bw.write("\n");
    }

    public void println(Object a) throws Exception {
        print(a);
        println();
    }

    public void flush() throws Exception {
        bw.flush();
    }
}
