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 $p_{i+1} p_{i+2} form a 90 degree angle. (1 \leq i \leq N - 1)$

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.

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.

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

见题面 Input 部分

见题面 Output 部分