Widespread

Source: AtCoder

Version: Phuoc Hung OJ Extended

Problem Statement

There are $N$ monsters with health $h_i$. In one explosion, choose one alive monster as the center. It loses $A$ health and every other alive monster loses $B$ health, where $A>B$. Find the minimum number of explosions needed to eliminate all monsters.

Input

The first line contains $N,A,B$. The next $N$ lines contain $h_i$.

Output

Print the minimum number of explosions.

Subtasks

• Subtask 1 — 20%: $N=1$.
• Subtask 2 — 30%: $1\le N\le1000$.
• Subtask 3 — 50%: $1\le N\le10^5$, $1\le B<A\le10^9$, $1\le h_i\le10^9$.

Examples

Input

4 5 3
8
7
4
2

Output

2

Explanation

Initially the health values are $8,7,4,2$.

• Center the first explosion at the monster with health $8$. The values become $3,4,1,-1$, so the last monster vanishes.
• Center the second explosion at the monster with health $4$. The remaining values become $0,-1,-2$, so all monsters vanish.

Thus two explosions are sufficient, and one explosion is not.