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 javax.imageio.ImageIO;
import java.awt.image.BufferedImage;
import java.io.*;
import java.math.BigInteger;
import java.net.PortUnreachableException;
import java.util.*;

// written by luchy0120

public class Main {
    public static void main(String[] args) throws Exception {

        new Main().run();
    }

    static int groups = 0;
    static int[] fa;
    static int[] sz;

    static void init(int n) {
        groups = n;
        fa = new int[n];
        for (int i = 1; i < n; ++i) {
            fa[i] = i;
        }
        sz = new int[n];
        Arrays.fill(sz, 1);
    }

    static int root(int p) {
        while (p != fa[p]) {
            fa[p] = fa[fa[p]];
            p = fa[p];
        }
        return p;
    }

    static void combine(int p, int q) {
        int i = root(p);
        int j = root(q);
        if (i == j) {
            return;
        }
        if (sz[i] < sz[j]) {
            fa[i] = j;
            sz[j] += sz[i];
        } else {
            fa[j] = i;
            sz[i] += sz[j];
        }
        groups--;
    }

    int child[];
    int color[],dfn[],low[],stack[],cnt[];
    boolean vis[];
    boolean iscut[];
    int deep,top,n,m,sum,ans;
    List<Integer> g[];
    int root = 0;
    //  无向图的强连通分量
    void tarjanNonDirect(int u1) {

        int stk[] = new int[10001];
        int fatk[] = new int[10001];
        int p = 0;
        stk[p] = u1;
        fatk[p] = -1;
        p= 1;
        ot: while(p>0) {
            int u  = stk[p-1];
            int fa = fatk[p-1];


            if(dfn[u]==0) {
                low[u] = dfn[u] = ++deep;
            }
            // stack[top++] = u;

            for (; h[u] != -1; h[u] = ne[h[u]]) {
                int v = to[h[u]];
                if (dfn[v] == 0) {
                    //tarjanNonDirect(v);

                    fatk[p] = u;
                    stk[p++] = v;
                    continue ot;
                } else {
                    low[u] = Math.min(low[u], dfn[v]);
                    // 没有特判是否直接指向父亲
                    // 回边，使用dfn【v】更新low【u】,因为可能是指向父亲，而父亲的low可能比较小
                }
            }
            --p;

            if (fa != -1) {
                low[fa] = Math.min(low[fa], low[u]);
                if (low[u] >= dfn[fa]) {
                    if (fa != root || ++child[fa] > 1) {     // 不是root，直接记为cut，是root，判断是否有两个儿子
                        iscut[fa] = true;
                    }
                    ++dcc_cnt;
                    // 一个割点可能会被多个点双共享
                    //  int z = -1;
                    //    do {
                    //        z = stack[--top];
                    //      dcc[dcc_cnt].add(z);
                    //    } while(z != v);
                    //   dcc[dcc_cnt].add(u);
                }


            }

        }
    }
    int gd = 0;
    int id =-1;
    int scc_cnt = 0;
    int sccno[];

//    void solve() {
//
//    }




//    int get_room(int i,int j){
//        return i/3*3 + j/3;
//    }

//    int a[][] = new int[9][9];
//    int space = 0;
//
//    boolean vis_row[][] = new boolean[9][10];
//    boolean vis_col[][] = new boolean[9][10];
//    boolean vis_room[][] = new boolean[9][10];
//    int val[][][] =new int[9][9][];
//    int prepare[][];
//
//    void dfs(int rt){
//
//    }

    int h[],to[],ne[];int ct =0;
    void add(int u,int v){
        // u--;v--;
        to[ct] = v;
        ne[ct] = h[u];
        h[u] = ct++;

    }

    int dcc_cnt = 0;
    int time = 0;








    private static double f(double x) {
        return Math.pow(Math.abs(x), 0.5) + (5*(Math.pow(x, 3)));
    }

    void dfs(int rt,int fa){
        size[rt]  =1;
        for(int i=h[rt];i!=-1;i=ne[i]){
            int v = to[i];
            if(v==fa) continue;
            dep[v] = dep[rt]+1;
            dfs(v,rt);
            size[rt] += size[v];
        }
    }

    int size[];int dep[];



    long get(int i,int i1,int j,int j1){
        return s[i1][j1] - s[i-1][j1] - s[i1][j-1] + s[i-1][j-1];
    }
    long mod = 1000000007;
    long sv(int i,int i1,int j,int j1,int qie){

        if(dp[i][i1][j][j1][qie]!=0) return dp[i][i1][j][j1][qie];
        if(qie==0) return 1;
        long t = 0;
        for(int k=i+1;k<=i1;++k){
            long num = get(i,k-1,j,j1);
            long num1 = get(k,i1,j,j1);
            if(num>0&&num1>0){
                t += sv(k,i1,j,j1,qie-1);
                t %= mod;
            }
        }
        for(int k=j+1;k<=j1;++k){
            long num = get(i,i1,j,k-1);
            long num1 = get(i,i1,k,j1);
            if(num>0&&num1>0){
                t += sv(i,i1,k,j1,qie-1);
                t %= mod;
            }
        }
        return dp[i][i1][j][j1][qie] = t;
    }

    long s[][];
    long dp[][][][][];
    public int ways(String[] p, int k) {
        int l  = p.length;
        int ll = p[0].length();

        dp = new long[l+1][l+1][ll+1][ll+1][k+1];
        s  = new long[l+1][ll+1];

        for(int i=1;i<=l;++i){
            for(int j=1;j<=ll;++j){
                int c = 0;
                if(p[i-1].charAt(j-1)=='A'){
                    c++;
                }
                s[i][j] = s[i-1][j] + s[i][j-1] - s[i-1][j-1] + c;
            }
        }

        return (int)sv(1,l,1,ll,k-1);







    }



    void solve() {
        int t =ni();
       ot: while(t-->0) {
            int n = ni();
            int a[] = na(n);
            int mi = 1000000000;
            int ma = -1;
            int d[] = new int[n];
            Set<Integer> st = new HashSet<>();
            for(int i=0;i<n;++i){
                mi = Math.min(mi,a[i]);
                ma = Math.max(ma,a[i]);
                st.add(a[i]);
                if(st.size()==ma-mi+1&&ma==i+1&&mi==1){
                    d[i] = 1;
                }

            }
            st.clear();
            mi = 1000000000;
            ma = -1;
            List<Integer> li = new ArrayList<>();
            for(int i=n-1;i>=0;--i){
                mi = Math.min(mi,a[i]);
                ma = Math.max(ma,a[i]);
                st.add(a[i]);
                if(ma-mi+1==st.size()&&mi==1&&ma==n-i){
                    if(i-1>=0&&d[i-1]==1){
                        li.add(i);
                    }
                }

            }
            println(li.size());
            for(int i=0;i<li.size();++i){
                println(li.get(i)+" "+(n-li.get(i)));
            }


        }



//        int t  =ni();
//        for(int i=0;i<t;++i){
//            int f[]  = na(3);
//            StringBuilder sb  =new StringBuilder();
//            if(f[1]>0){
//                int v = 0;
//
//
//                    for(int j=0;j<f[0]+1;++j){
//                        sb.append(0);
//                    }
//
//
//
//
//                    for(int j=0;j<f[2]+1;++j){
//                        sb.append(1);
//                    }
//
//                    f[1]--;
//
//                for(int j=0;j<f[1];++j){
//                    sb.append(v); v ^= 1;
//                }
//
//                println(sb);
//            }else{
//                if(f[0]>0){
//
//                    for(int j=0;j<f[0]+1;++j){
//                        sb.append(0);
//                    }
//                    println(sb);
//                }
//                if(f[2]>0){
//
//                    for(int j=0;j<f[2]+1;++j){
//                        sb.append(1);
//                    }
//                    println(sb);
//                }
//
//
//            }
//
//
//        }

    }


      //  println(width);
//      //  println(height);
//        int i  =ni();
//        int j  =ni();


//        for(int i=0;i<height;++i){
//            for(int j=0;j<width;++j){
//               int me =  bi.getRGB(i,j);
//               print(me==-1?0:1);
//            }
//            println();
//        }

//        int minx = bi.getMinX();
//        int miny = bi.getMinY();
//        System.out.println("width=" + width + ",height=" + height + ".");
//        System.out.println("minx=" + minx + ",miniy=" + miny + ".");
//        int b[][][] = new int[64][64][3];
//
//        for (int i = minx; i < width; i++) {
//            for (int j = miny; j < height; j++) {
//                int pixel = bi.getRGB(i, j);
//              //  print(pixel);
//               // b[j][i] = pixel;
//
//                b[j][i][0] = (pixel & 0xff0000) >> 16;
//                b[j][i][1] = (pixel & 0xff00) >> 8;
//                b[j][i][2] = (pixel & 0xff);
//
//            }
//            println();
//        }
//
//        for(int i=0;i<64;++i){
//            print("\"");
//            for(int j=0;j<64;++j){
//                print(b[i][j][0]<=50?"*":" ");
//            }
//            println("\",");
//        }
//        //println(b[0][0]);


//
//
//
//
//
//            }
//        }
    //    print("No");




//        int n = ni();
//        int m  = n*(n+1)/2;
//        int k = ni();
//        int p = 0;
//
//        double x[] = new double[n];
//        double y[] = new double[n];
//
//        for(int i=0;i<n;++i){
//            x[i] = nd();
//            y[i] = nd();
//        }
//
//        List<Item> li = new ArrayList<>();
//        for(int i=0;i<n;++i){
//            for(int j=i+1;j<n;++j){
//               double r =  (x[i]-x[j])*(x[i]-x[j]) + (y[i]-y[j])*(y[i]-y[j]);
//               li.add(new Item(r,i,j));
//            }
//        }
//        Collections.sort(li,(xx,yy)->Double.compare(xx.s,yy.s));
//
//        init(n + 1);
//
//        int s = 0;
//        int c = n;
//        for (int i = 0; i < li.size(); ++i) {
//            int p1 = li.get(i).a;
//            int p2 = li.get(i).b;
//            if (root(p1) != root(p2)) {
//                combine(p1, p2);
//                c--;
//                if(c==k-1){
//                    print(roundS(Math.sqrt(li.get(i).s),2));
//                    break;
//                }
//            }
//        }

  //  }
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//    }


//    static long mul(long a, long b, long p)
//    {
//        long res=0,base=a;
//        while(b>0)
//        {
//            if((b&1L)>0)
//                res=(res+base)%p;
//            base=(base+base)%p;
//            b>>=1;
//        }
//        return res;
//    }


    static long mod_pow(long k,long n,long p){
        long res = 1L;
        long temp = (k%p+p)%p;
        while(n!=0L){
            if((n&1L)==1L){
                res = ((res*temp)%p+p)%p;
            }
            temp = ((temp * temp)%p+p)%p;
            n = n>>1L;
        }
        return res%p;
    }
    public static String roundS(double result, int scale){
        String fmt = String.format("%%.%df", scale);
        return String.format(fmt, result);
    }


//    void solve() {
//
//        for(int i=0;i<9;++i) {
//            for (int j = 0; j < 9; ++j) {
//                int v = ni();
//                a[i][j] = v;
//                if(v>0) {
//                    vis_row[i][v] = true;
//                    vis_col[j][v] = true;
//                    vis_room[get_room(i, j)][v] = true;
//                }else{
//                    space++;
//                }
//            }
//        }
//
//
//        prepare = new int[space][2];
//
//        int p = 0;
//
//        for(int i=0;i<9;++i) {
//            for (int j = 0; j < 9; ++j) {
//                if(a[i][j]==0){
//                    prepare[p][0] = i;
//                    prepare[p][1]= j;p++;
//                    List<Integer> temp =new ArrayList<>();
//                    for(int k=1;k<=9;++k){
//                        if(!vis_col[j][k]&&!vis_row[i][k]&&!vis_room[get_room(i,j)][k]){
//                            temp.add(k);
//                        }
//                    }
//                    int sz = temp.size();
//                    val[i][j] = new int[sz];
//                    for(int k=0;k<sz;++k){
//                        val[i][j][k] = temp.get(k);
//                    }
//                }
//            }
//        }
//        Arrays.sort(prepare,(x,y)->{
//           return Integer.compare(val[x[0]][x[1]].length,val[y[0]][y[1]].length);
//        });
//        dfs(0);
//
//
//
//
//
//
//
//
//
//
//    }




    InputStream is;
    PrintWriter out;

    void run() throws Exception {
        //is = new FileInputStream(new File("C:\\Users\\Luqi\\Downloads\\P3387_9.in"));
        is = System.in;
        out = new PrintWriter(System.out);

        solve();
        out.flush();
    }

    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;

    private int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) return -1;
        }
        return inbuf[ptrbuf++];
    }

    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }

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

    private double nd() {
        return Double.parseDouble(ns());
    }

    private char nc() {
        return (char) skip();
    }

    private char ncc() {
        int b = readByte();
        return (char) b;
    }

    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private String nline() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!isSpaceChar(b) || b == ' ') {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[][] nm(int n, int m) {
        char[][] a = new char[n][];
        for (int i = 0; i < n; i++) a[i] = ns(m);
        return a;
    }

    private int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = ni();
        return a;
    }

    private long[] nal(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = nl();
        return a;
    }

    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) {
        }
        ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') num = (num << 3) + (num << 1) + (b - '0');
            else return minus ? -num : num;
            b = readByte();
        }
    }

    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) {
        }
        ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') num = num * 10 + (b - '0');
            else return minus ? -num : num;
            b = readByte();
        }
    }

    void print(Object obj) {
        out.print(obj);
    }

    void println(Object obj) {
        out.println(obj);
    }

    void println() {
        out.println();
    }

    void printArray(int a[],int from){
        int l = a.length;
        for(int i=from;i<l;++i){
            print(a[i]);
            if(i!=l-1){
                print(" ");
            }
        }
        println();
    }

    void printArray(long a[],int from){
        int l = a.length;
        for(int i=from;i<l;++i){
            print(a[i]);
            if(i!=l-1){
                print(" ");
            }
        }
        println();
    }
}