{"raw_statement":[{"iden":"statement","content":"Even though he is the head of the Shitalian Mafia, Shi doesn't like bloodshed and punishes his subordinates if they kill innocent people. That is why the death report is always written in the following way: #cf_span(class=[tex-font-style-underline], body=[\"We killed x% of the innocent people\"]).\n\nShi wants to know the smallest number of innocent people that must have been in that place so that *exactly* x% of the innocent people have died.\n\nFor instance, if we have x = 35%. In this case we had 20 people, and 7 were victims, because 35% of 20 is 7. That is the minimum possible.\n\nThere is a single number 0 ≤ x ≤ 100 with at most 15 decimal places.\n\nPrint the number sought by Shi.\n\n"},{"iden":"input","content":"There is a single number 0 ≤ x ≤ 100 with at most 15 decimal places."},{"iden":"output","content":"Print the number sought by Shi."},{"iden":"examples","content":"Input35Output20Input50.0Output2Input7.500Output40Input35.123456789Output100000000000"}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ n, d \\in \\mathbb{Z}^+ $, with $ 1 \\leq n \\leq 10^5 $, $ 1 \\leq d \\leq 10^9 $.  \nLet $ A = (a_1, a_2, \\dots, a_n) \\in \\mathbb{Z}^n $ be the initial rating vector of $ n $ users.  \n\nLet $ \\sigma: \\{1, \\dots, n\\} \\to \\{1, \\dots, n\\} $ be a permutation such that $ a_{\\sigma(1)} > a_{\\sigma(2)} > \\dots > a_{\\sigma(n)} $ (i.e., users sorted in descending order of initial ratings).  \n\nLet $ x_i \\in \\mathbb{Z} $ denote the net number of contests (positive for increases, negative for decreases) applied to user $ i $.  \nEach contest changes a user’s rating by $ \\pm d $, so the final rating of user $ i $ is $ a_i + x_i \\cdot d $.  \n\n**Constraints**  \n1. All final ratings must be distinct:  \n   $$\n   a_i + x_i d \\neq a_j + x_j d \\quad \\forall i \\neq j\n   $$  \n2. After contests, user $ i $ must have the $ i $-th greatest rating (i.e., the final ratings must be strictly decreasing with user index):  \n   $$\n   a_1 + x_1 d > a_2 + x_2 d > \\dots > a_n + x_n d\n   $$  \n3. Each $ x_i \\in \\mathbb{Z} $, and the total number of contests is $ \\sum_{i=1}^n |x_i| $ (each contest affects exactly one user).  \n\n**Objective**  \nMinimize $ \\sum_{i=1}^n |x_i| $, subject to the above constraints.","simple_statement":"You are given n users with initial ratings a1, a2, ..., an. In each contest, every user's rating changes by exactly +d or -d. You want to assign a unique final rating to each user so that the user with index i ends up with the i-th highest rating. Find the minimum number of contests needed.","has_page_source":false}