Given an array ~a~ of ~n~ integers, count how many subarrays of length exactly ~x~ contain at least ~k~ distinct values.

Remember that a subarray is a contiguous section of the array.

Input

The first line contains three integers ~n~, ~x~, and ~k~.

The second line contains ~n~ integers ~a_1, a_2, \dots, a_n~.

Output

Print a single integer: the number of subarrays of length exactly ~x~ that contain at least ~k~ distinct values.

Constraints

• ~1 \le k \le x \le n \le 2 \cdot 10^5~
• ~-10^9 \le a_i \le 10^9~

Example 1

Input

8 4 3
1 1 2 3 2 2 1 4

Output

4

Explanation

The five subarrays of length ~4~ are:

• ~[1, 1, 2, 3]~, which has ~3~ distinct values;
• ~[1, 2, 3, 2]~, which has ~3~ distinct values;
• ~[2, 3, 2, 2]~, which has ~2~ distinct values;
• ~[3, 2, 2, 1]~, which has ~3~ distinct values;
• ~[2, 2, 1, 4]~, which has ~3~ distinct values.

So the answer is ~4~.