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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class e {
	public static void main(String[] args) throws IOException {
		FastScanner in = new FastScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		
		int n = in.nextInt(), q = in.nextInt();
		double[] arr = new double[n];
		for(int i=0;i<n;i++)
			arr[i] = in.nextDouble();
		ST st = new ST(arr);
		
		while(q --> 0) {
			int type = in.nextInt();
			if(type == 1) {
				int l1 = in.nextInt()-1, r1 = in.nextInt()-1, l2 = in.nextInt()-1, r2 = in.nextInt()-1;
				
				double e1 = st.query(l1, r1) / (double)(r1-l1+1);
				double e2 = st.query(l2, r2) / (double)(r2-l2+1);
				
				st.multiply(l1, r1, (r1-l1+1-1) / (double)(r1-l1+1));
				st.add(l1, r1, e2 / (double)(r1-l1+1));

				st.multiply(l2, r2, (r2-l2+1-1) / (double)(r2-l2+1));
				st.add(l2, r2, e1 / (double)(r2-l2+1));
			} else {
				int l = in.nextInt()-1, r = in.nextInt()-1;
				out.println(st.query(l, r));
			}
		}
		out.close();
	}
	static class ST {
		double[] mult, add, sum;
		int n;
		ST(double[] vs) {
			n = vs.length;
			mult = new double[4*n];
			Arrays.fill(mult, 1);
			add = new double[4*n];
			sum = new double[4*n];
			init(vs, 1, 0, n-1);
		}
		void init(double[] init, int idx, int l, int r) {
			if(l == r) {
				sum[idx] = init[l];
				return;
			}
			int mid = (l+r)/2;
			init(init, idx*2, l, mid);
			init(init, idx*2+1, mid+1, r);
			sum[idx] = sum[idx*2] + sum[idx*2+1];
		}
		void prop(int idx, int l, int r) {
			mult[idx*2] *= mult[idx];
			add[idx*2] *= mult[idx];
			mult[idx*2+1] *= mult[idx];
			add[idx*2+1] *= mult[idx];
			mult[idx] = 1;

			add[idx*2] += add[idx];
			add[idx*2+1] += add[idx];
			add[idx] = 0;
		}
		void fix(int idx, int l, int r) {
			int mid = (l+r)/2;
			sum[idx] = get(idx*2, l, mid) + get(idx*2+1, mid+1, r);
		}
		double get(int idx, int l, int r) {
			return sum[idx] * mult[idx] + (add[idx] * (r-l+1));
		}
		void multiply(int l, int r, double v) {
			multiply(1, 0, n-1, l, r, v);
		}
		void multiply(int idx, int l, int r, int ul, int ur, double v) {
			if(r < ul || l > ur)
				return;
			if(l >= ul && r <= ur) {
				add[idx] *= v;
				mult[idx] *= v;
				return;
			}
			prop(idx, l, r);
			int mid = (l+r)/2;
			multiply(idx*2, l, mid, ul, ur, v);
			multiply(idx*2+1, mid+1, r, ul, ur, v);
			fix(idx, l, r);
		}
		void add(int l, int r, double v) {
			add(1, 0, n-1, l, r, v);
		}
		void add(int idx, int l, int r, int ul, int ur, double v) {
			if(r < ul || l > ur)
				return;
			if(l >= ul && r <= ur) {
				add[idx] += v;
				return;
			}
			prop(idx, l, r);
			int mid = (l+r)/2;
			add(idx*2, l, mid, ul, ur, v);
			add(idx*2+1, mid+1, r, ul, ur, v);
			fix(idx, l, r);
		}
		double query(int l, int r) {
			return query(1, 0, n-1, l, r);
		}
		double query(int idx, int l, int r, int ul, int ur) {
			if(r < ul || l > ur)
				return 0;
			if(l >= ul && r <= ur) {
				return get(idx, l, r);
			}
			prop(idx, l, r);
			int mid = (l+r)/2;
			double ans = 0;
			ans += query(idx*2, l, mid, ul, ur);
			ans += query(idx*2+1, mid+1, r, ul, ur);
			fix(idx, l, r);
			return ans;
		}
	}
	static class FastScanner {
	    BufferedReader br;
	    StringTokenizer st;
		
	    public FastScanner(InputStream i) {
	        br = new BufferedReader(new InputStreamReader(i));
	        st = new StringTokenizer("");
	    }
				
	    public String next() throws IOException {
	        if(st.hasMoreTokens())
	            return st.nextToken();
	        else
	            st = new StringTokenizer(br.readLine());
	        return next();
	    }

	    public int nextInt() throws IOException {
	        return Integer.parseInt(next());
	    }
	    
	    public long nextLong() throws IOException {
	    	return Long.parseLong(next());
	    }
	    
	    public double nextDouble() throws IOException {
	        return Double.parseDouble(next());
	    }
	}
}