A11397 | Eyes Closed

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.

The first line contains two integers $n,q$ ( $2<=n<=10^{5},1<=q<=10^{5}$ ) — the number of elements in the array and the number of queries you need to handle.

The second line contains $n$ integers $a_{i}$ ( $1<=a_{i}<=10^{9}$ ) — 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.

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  where $x$ is jury's answer and $y$ is yours.