1355_E. Restorer Distance
You have to restore the wall. The wall consists of N pillars of bricks, the height of the i-th pillar is initially equal to h_{i}, the height is measured in number of bricks. After the restoration all the N pillars should have equal heights.

You are allowed the following operations:

  * put a brick on top of one pillar, the cost of this operation is A;
  * remove a brick from the top of one non-empty pillar, the cost of this operation is R;
  * move a brick from the top of one non-empty pillar to the top of another pillar, the cost of this operation is M.



You cannot create additional pillars or ignore some of pre-existing pillars even if their height becomes 0.

What is the minimal total cost of restoration, in other words, what is the minimal total cost to make all the pillars of equal height?

Input

The first line of input contains four integers N, A, R, M (1 ≤ N ≤ 10^{5}, 0 ≤ A, R, M ≤ 10^{4}) — the number of pillars and the costs of operations.

The second line contains N integers h_{i} (0 ≤ h_{i} ≤ 10^{9}) — initial heights of pillars.

Output

Print one integer — the minimal cost of restoration.

Examples

Input


3 1 100 100
1 3 8


Output


12


Input


3 100 1 100
1 3 8


Output


9


Input


3 100 100 1
1 3 8


Output


4


Input


5 1 2 4
5 5 3 6 5


Output


4


Input


5 1 2 2
5 5 3 6 5


Output


3
```python
#!/usr/bin/env python3
import io
import os
from bisect import bisect
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
def get_str():
    return input().decode().strip()
def rint():
    return map(int, input().split())
def oint():
    return int(input())

def find_lu_value(th):
    hi = bisect(h, th) - 1
    lv = th * (hi + 1) - ps[hi]
    uv = (ps[n - 1] - ps[hi]) - (n - 1 - hi) * th
    return lv, uv

def calc_cost(th):
    cost = 0
    l, u = find_lu_value(th)
    if l > u:
        cost += u * m + (l - u) * a
    else:
        cost += l * m + (u - l) * r
    return cost

def calc_prefixsum(h):
    ps = [h[0]]
    for i in range(1, n):
        ps.append(h[i] + ps[-1])
    return ps

n, a, r, m = rint()
h = list(rint())

m = min(m, a + r)
h.sort()
ps = calc_prefixsum(h)
ans = 10**99

lv = h[0]
rv = h[-1]


ans = min(ans, calc_cost(lv), calc_cost(rv), calc_cost(lv+1))
while rv-lv >= 2:
    mv = (rv-lv)//2 + lv
    mc = calc_cost(mv)
    rc = calc_cost(mv+1)
    ans = min(ans,  rc, mc)
    if mc < rc:
        rv = mv
    elif mc > rc:
        lv = mv
print(ans)

```