B"Vova decided to clean his room. The room can be represented as the coordinate axis OX . There are n piles of trash in the room, coordinate of the i -th pile is the integer p_i . All piles have different coordinates. Let's define a total cleanup as the following process. The goal of this process is to collect all the piles in no more than two different x coordinates. To achieve this goal, Vova can do several (possibly, zero) moves. During one move, he can choose some x and move all piles from x to x+1 or x-1 using his broom. Note that he can't choose how many piles he will move. Also, there are two types of queries: Note that it is possible that there are zero piles of trash in the room at some moment. Vova wants to know the minimum number of moves he can spend if he wants to do a total cleanup before any queries. He also wants to know this number of moves after applying each query. Queries are applied in the given order. Note that the total cleanup doesn't actually happen and doesn't change the state of piles. It is only used to calculate the number of moves. For better understanding, please read the Notes section below to see an explanation for the first example. The first line of the input contains two integers n and q ( 1 <= n, q <= 10^5 ) -- the number of piles in the room before all queries and the number of queries, respectively. The second line of the input contains n distinct integers p_1, p_2, ... , p_n ( 1 <= p_i <= 10^9 ), where p_i is the coordinate of the i -th pile. The next q lines describe queries. The i -th query is described with two integers t_i and x_i ( 0 <= t_i <= 1; 1 <= x_i <= 10^9 ), where t_i is 0 if you need to remove a pile from the coordinate x_i and is 1 if you need to add a pile to the coordinate x_i . It is guaranteed that for t_i = 0 there is such pile in the c"...