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 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. 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. 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.