Problem Statement

You are given a sequence ~A = (A_1, A_2, \dots, A_N)~ of length ~N~ consisting of positive integers, and integers ~x~ and ~y~ .
Determine whether it is possible to place ~N+1~ points ~p_1, p_2, \dots, p_N, p_{N+1}~ in the ~xy~ -coordinate plane to satisfy all of the following conditions. (It is allowed to place two or more points at the same coordinates.)

• ~p_1 = (0, 0)~ .
• ~p_2 = (A_1, 0)~ .
• ~p_{N+1} = (x, y)~ .
• The distance between the points ~p_i~ and ~p_{i+1}~ is ~A_i~ . ( ~1 \leq i \leq N~ )
• The segments ~p_i p_{i+1}~ and ~p_{i+1} p_{i+2}~ form a ~90~ degree angle. ( ~1 \leq i \leq N - 1~ )

Constraints

• ~2 \leq N \leq 10^3~
• ~1 \leq A_i \leq 10~
• ~|x|, |y| \leq 10^4~
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

~N~ ~x~ ~y~ ~A_1~ ~A_2~ ~\dots~ ~A_N~

Output

If it is possible to place ~p_1, p_2, \dots, p_N, p_{N+1}~ to satisfy all of the conditions in the Problem Statement, print Yes ; otherwise, print No .

Sample Input 1

3 -1 1
2 1 3

Sample Output 1

Yes

The figure below shows a placement where ~p_1 = (0, 0)~ , ~p_2 = (2, 0)~ , ~p_3 = (2, 1)~ , and ~p_4 = (-1, 1)~ . All conditions in the Problem Statement are satisfied.

Sample Input 2

5 2 0
2 2 2 2 2

Sample Output 2

Yes

Letting ~p_1 = (0, 0)~ , ~p_2 = (2, 0)~ , ~p_3 = (2, 2)~ , ~p_4 = (0, 2)~ , ~p_5 = (0, 0)~ , and ~p_6 = (2, 0)~ satisfies all the conditions. Note that multiple points may be placed at the same coordinates.

Sample Input 3

4 5 5
1 2 3 4

Sample Output 3

No

Sample Input 4

3 2 7
2 7 4

Sample Output 4

No

Sample Input 5

10 8 -7
6 10 4 1 5 9 8 6 5 1

Sample Output 5

Yes