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E. Eyes Closed

time limit per test

2.5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVasya 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 *l*1, *r*1, *l*2, *r*2 — boundaries of two non-intersecting segments. After that he swaps one random element from the [*l*1, *r*1] segment with another random element from the [*l*2, *r*2] 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* ≤ 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, *l*1, *r*1, *l*2, *r*2 (1 ≤ *l*1 ≤ *r*1 ≤ *n*, 1 ≤ *l*2 ≤ *r*2 ≤ *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 [*l*1, *r*1], [*l*2, *r*2] 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 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

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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