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.

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 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

inputFormat

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.

outputFormat

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

样例

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

3.0000000000
3.0000000000

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