E. Eyes Closedtime limit per test2.5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard 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 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.InputThe 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. OutputFor 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.ExamplesInput4 41 1 2 21 2 2 3 32 1 21 1 2 3 42 1 2Output3.00000003.0000000Input10 51 1 1 1 1 2 2 2 2 21 1 5 6 102 1 51 1 5 6 101 1 5 6 102 6 10Output6.00000008.0400000Input10 101 2 3 4 5 6 7 8 9 101 1 5 6 101 1 5 6 102 1 51 1 3 6 92 1 31 5 7 8 101 1 1 10 102 1 52 7 102 1 10Output23.000000014.000000028.013333321.573333355.0000000
Input4 41 1 2 21 2 2 3 32 1 21 1 2 3 42 1 2
Output3.00000003.0000000
['data structures', 'probabilities', '*2300']