MCPT is selling MCP Tea! They want to determine their total revenue ~R~ if they set the price to ~P~. It is also known that the quantity of products sold ~Q~ is related to the price ~P~ by the linear equation ~A \cdot Q + B \cdot P = C~, where ~A, B, C~ are integers. In addition, MCPT knows that the revenue ~R~ for a price ~P~ is given by ~R(P) = P \cdot Q~.

MCPT wishes to know for ~N~ different prices ~P_i~ whether the price belongs to the part of the demand curve that is elastic or inelastic. A price ~P_1~ belongs to the inelastic part if there exists a ~P_2~ such that ~P_2 > P_1~ and ~R(P_2) > R(P_1)~, otherwise it is elastic. Can you help MCPT?

Input Specification

The first line will contain 4 integers ~N\ (1 \le N \le 10^5), A, B, C\ (0 \le A, B, C \le 10^5)~.

The next ~N~ lines will contain an integer ~P_i\ (0 \le P_i \le 10^5)~.

It is guaranteed that ~A~ and ~B~ will not BOTH be zero.

Output Specification

On each line output elastic or inelastic if price ~P_i~ belongs to the elastic or inelastic part of the curve.

Sample Input

4 1 1 5
1
2
3
4

Sample Output

inelastic
inelastic
elastic
elastic