B"There are n people (numbered from 1 to n ) signed up for a doctor's appointment. The doctor has to choose in which order he will appoint these people. The i -th patient should be appointed among the first p_i people. There are also m restrictions of the following format: the i -th restriction is denoted by two integers (a_i, b_i) and means that the patient with the index a_i should be appointed earlier than the patient with the index b_i . For example, if n = 4 , p = [2, 3, 2, 4] , m = 1 , a = [3] and b = [1] , then the only order of appointment of patients that does not violate the restrictions is [3, 1, 2, 4] . For n =3 , p = [3, 3, 3] , m = 0 , a = [] and b = [] , any order of appointment is valid. For each patient, calculate the minimum position in the order that they can have among all possible orderings that don't violate the restrictions. The first line contains two integers n and m ( 1 <= n <= 2000 ; 0 <= m <= 2000 ). The second line contains n integers p_1, p_2, ... , p_n ( 1 <= p_i <= n ). Then m lines follow. The i -th of them contains two integers a_i and b_i ( 1 <= a_i, b_i <= n ; a_i ne b_i ). All pairs of (a_i, b_i) are distinct (i. xe2 x80 x89e. if i ne j , then either a_i ne a_j , b_i ne b_j , or both). Additional constraint on the input: there is at least one valid order of patients. Print n integers, where i -th integer is equal to the minimum position of i -th patient in the order, among all valid orders. Positions in the order are numbered from 1 to n . In the first example, [3, 1, 2, 4] the only one valid order, so the minimum position of each patient is equal to their position in this order. In the second example, any order is valid, so any patient can be appointed first. In the third example, ther"...