Problem: Vasya and Petya were tired of studying so they decided to play a game. Before the game begins Vasya looks at array a consisting of n integers. As soon as he remembers all elements of a the game begins. Vasya closes his eyes and Petya does q actions of one of two types:

1) Petya says 4 integers l1, r1, l2, r2 — boundaries of two non-intersecting segments. After that he swaps one random element from the [l1, r1] segment with another random element from the [l2, r2] segment.

2) Petya asks Vasya the sum of the elements of a in the [l, r] segment.

Vasya is a mathematician so he answers Petya the mathematical expectation of the sum of the elements in the segment.

Your task is to write a program which will answer the second type questions as Vasya would do it. In other words your program should print the mathematical expectation of the sum of the elements of a in the [l, r] segment for every second type query.

Input

The first line contains two integers n, q (2 ≤ n ≤ 105, 1 ≤ q ≤ 105) — the number of elements in the array and the number of queries you need to handle.

The second line contains n integers ai (1 ≤ ai ≤ 109) — elements of the array.

The next q lines contain Petya's actions of type 1 or 2.

If it is a type 1 action then the line contains 5 integers 1, l1, r1, l2, r2 (1 ≤ l1 ≤ r1 ≤ n, 1 ≤ l2 ≤ r2 ≤ n).

If it is a type 2 query then the line contains 3 integers 2, l, r (1 ≤ l ≤ r ≤ n).

It is guaranteed that there is at least one type 2 query and segments [l1, r1], [l2, r2] don't have common elements. 

Output

For each type 2 query print one real number — the mathematical expectation of the sum of elements in the segment.

Your answer will be considered correct if its absolute or relative error doesn't exceed 10 - 4 — formally, the answer is correct if <image> where x is jury's answer and y is yours.

Examples

Input

4 4
1 1 2 2
1 2 2 3 3
2 1 2
1 1 2 3 4
2 1 2


Output

3.0000000
3.0000000


Input

10 5
1 1 1 1 1 2 2 2 2 2
1 1 5 6 10
2 1 5
1 1 5 6 10
1 1 5 6 10
2 6 10


Output

6.0000000
8.0400000


Input

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


Output

23.0000000
14.0000000
28.0133333
21.5733333
55.0000000

Solution (in JAVA):

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


public class Main {
    private static final int MAX = 100*1000 + 10;
    private static int n;
    private static int [] I = new int[MAX];
    private static double [] ST = new double[MAX*4];
    private static double [] A = new double[MAX*4];
    private static double [] B = new double[MAX*4];
    private static boolean [] LA = new boolean[MAX*4];

    private static void build(int node,int s,int e) {
        LA[node] = false;
        A[node] = 1;
        if(s == e) {
            ST[node] = I[s];
            return;
        }
        int m = (s + e) >> 1,left = node << 1,right = left | 1;
        build(left,s,m);
        build(right,m+1,e);
        ST[node] = ST[left] + ST[right];
    }

    private static void update(int node,int s,int e,double mul,double val) {
        ST[node] = ST[node]*mul + (val*(e-s+1));
        A[node] *= mul;
        B[node] = B[node] * mul + val;
        LA[node] = true;
    }

    private static void push(int node,int s,int e) {
        if(!LA[node]) return;
        int m = (s + e) >> 1,left = node << 1,right = left | 1;
        update(left,s,m,A[node],B[node]);
        update(right,m+1,e,A[node],B[node]);

        LA[node] = false;
        A[node] = 1;
        B[node] = 0;
    }

    private static void updateRange(int node,int s,int e,int l,int r,double mul,double val) {
        if(l <= s && e <= r) {
            update(node,s,e,mul,val);
            return;
        }

        push(node,s,e);
        int m = (s + e) >> 1,left = node << 1,right = left | 1;
        if(r <= m) updateRange(left,s,m,l,r,mul,val);
        else if(m < l) updateRange(right,m+1,e,l,r,mul,val);
        else {
            updateRange(left,s,m,l,m,mul,val);
            updateRange(right,m+1,e,m+1,r,mul,val);
        }
        ST[node] = ST[left] + ST[right];
    }

    private static double getRange(int node,int s,int e,int l,int r) {
        if(l <= s && e <= r) return ST[node];
        push(node,s,e);
        int m = (s + e) >> 1,left = node << 1,right = left | 1;
        if(r <= m) return getRange(left,s,m,l,r);
        if(m < l) return getRange(right,m+1,e,l,r);
        return getRange(left,s,m,l,m) + getRange(right,m+1,e,m+1,r);
    }

    public static void main(String[] args) throws Exception{
        IO io = new IO(null,null);
        int m;
        n = io.getNextInt();
        m = io.getNextInt();

        for (int i = 1;i <= n;i++)
            I[i] = io.getNextInt();

        build(1,1,n);

        while (m-- > 0) {
            int type = io.getNextInt();
            if(type == 1) {
                int l1 = io.getNextInt(),r1 = io.getNextInt();
                int l2 = io.getNextInt(),r2 = io.getNextInt();
                double a = getRange(1,1,n,l1,r1)/(r1-l1+1),b = getRange(1,1,n,l2,r2)/(r2-l2+1);
                double L1 = r1-l1+1,L2 = r2-l2+1;

                updateRange(1,1,n,l1,r1,(L1-1)/L1,b/L1);
                updateRange(1,1,n,l2,r2,(L2-1)/L2,a/L2);

            }
            else {
                int l = io.getNextInt(),r = io.getNextInt();
                io.print(getRange(1,1,n,l,r),10);
                io.println("");
            }
        }
        io.close();
    }
}






class IO{
    private BufferedReader br;
    private StringTokenizer st;
    private PrintWriter writer;
    private String inputFile,outputFile;

    public String getNext() throws FileNotFoundException, IOException{
        while(st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    public String getNextLine() throws FileNotFoundException, IOException{
        return br.readLine().trim();
    }

    public int getNextInt() throws FileNotFoundException, IOException{
        return Integer.parseInt(getNext());
    }
    public long getNextLong() throws FileNotFoundException, IOException{
        return Long.parseLong(getNext());
    }

    public void print(double x,int num_digits) throws  IOException{
        writer.printf("%." + num_digits + "f" ,x);
    }
    public void println(double x,int num_digits) throws  IOException{
        writer.printf("%." + num_digits + "f\n" ,x);
    }
    public void print(Object o) throws  IOException{
        writer.print(o.toString());
    }

    public void println(Object o) throws  IOException{
        writer.println(o.toString());
    }
    public IO(String x,String y) throws FileNotFoundException, IOException{
        inputFile = x;
        outputFile = y;
        if(x != null) br = new BufferedReader(new FileReader(inputFile));
        else br = new BufferedReader(new InputStreamReader(System.in));
        if(y != null) writer = new PrintWriter(new BufferedWriter(new FileWriter(outputFile)));
        else writer = new PrintWriter(new OutputStreamWriter(System.out));
    }

    protected void close() throws IOException{
        br.close();
        writer.close();
    }
}