The problem of finding the next term of a given sequence of numbers is usually proposed in QI tests. We want to construct a method and a codification that allow us to know all the sequence from the first N terms. Let S = (Si)i∈IN denote a sequence of real numbers whose i-order term is Si. We codify a constant sequence with the following operator: S=[n] meaningthat Si =n ∀i∈IN, where n ∈ Z. We also define the following operators on a given sequence of numbers S = (Si)i∈IN: { V =[m+S] meaningthat Vi = m Vi−1 + Si−1 { V =[m∗S] meaningthat Vi = m∗S1 Vi−1 ∗ Si ,i=1 ; , i > 1 ,i=1 ; , i > 1 where m ∈ IN. For example we have the following codifications: [2+[1]] = 2,3,4,5,6··· [1+[2+[1]]] = 1,3,6,10,15,21,28,36··· [2∗[1+[2+[1]]]]=2,6,36,360,5400,113400··· [2∗[5+[−2]]]=10,30,30,−30,90,−450,3150··· Given a sequence of N integer numbers and an integer M, the problem is to write the codification that generate the sequence and have at most M operators. We have that 2 ≤ N ≤ 51 and 1 ≤ M ≤ 50. Input The input file contains several test cases. For each of them, the program input is a single line containing M followed by the list of first terms of the sequence. The terms of the given sequence are positive (in the interval [1, 200000]) or negative integers (in the interval [-200000, -1]), and their number N can differ but it is always greater than M. Output For each test case, the program output is a single line containing the codification without any space. If there exists no solution with at most M operators, the output must be ‘[0]’. Examples Input 2 2 3 4 3 1 3 6 10 15 4 2 6 36 360 5400 113400 [2*[1+[2+[1]]]] Sample Input 3 10 30 30 -30 90 -450 3150 2 2 6 36 360 5400 113400 Sample Output [2*[5+[-2]]] [0] Output [2+[1]] [1+[2+[1]]]