# Rice Hub

# Rice Hub

In the countryside, you can find a long straight road known as the Rice Way. Along this road there are **R** rice fields. Each field is located at an integer coordinate between **1** and **L** inclusive. The rice fields will be presented in non-decreasing order of their coordinates. Formally, for **0** ≤ **i** < **R**, rice field **i** is at coordinate `X`

. You may assume that _{i}**1** ≤ `x`

≤ ... ≤ _{0}`x`

≤ _{R-1}**L**.

Please note that multiple rice fields may share the same coordinate.

We plan to construct a single rice hub as a common place to store as much of the harvest as possible. As with the rice fields, the hub has to be at an integer coordinate between **1** and **L**, inclusive. The rice hub can be at any location, including one that already contains one or more rice fields.

Each rice field produces exactly 1 truckload of rice every harvest season. To transport the rice to the hub, the city has to hire a truck driver. The driver charges **1** Baht to transport a truckload of rice per unit of distance towards the hub. In other words, the cost of transporting rice from a given field to the rice hub is numerically equal to the difference between their coordinates.

Unfortunately, our budget for this season is tight: we may only spend at most **B** Baht on transportation.
Your task is to help us strategically place the hub to gather as much rice as possible.

#### Input

First line contains three integers **R**, **L** and **B**, **R** - the number of rice fields, the fields are numbered from **0** till **R** - **1**, **L** - the maximum coordinate, **B** - the budget (**1** ≤ **R** ≤ **100000**, **1** ≤ **L** ≤ `10`

, ^{9}**0** ≤ **B** ≤ **2** *`10`

).^{15}

In the next **R** lines given **R** integers `X`

- the coordinate of _{i}**i**-th field, all integers are sorted in nondecreasing order.

#### Output

Print the maximum number of truckloads of rice that can be transported to the hub within the budget.

16 93 1 5 10 15 20 25 31 35 40 45 50 55 59 65 70 75 80

1