AT_abc480_c [ABC480C] Self-Stopping Shower

Takahashi is using a shower at a public bath. This shower has a button. If the button is pressed at time $ t $ , hot water comes out for $ K $ seconds, from time $ t $ to time $ t+K $ . Even if the button is pressed again while hot water is coming out, hot water comes out for $ K $ seconds from the time the button was last pressed. There are $ N $ Aokis, each of whom presses the button once. The $ i $ -th Aoki presses the button at time $ A_i $ . Find the minimum number of times Takahashi needs to press the button so that hot water is always coming out from time $ 0 $ to time $ T $ . Here, hot water is considered to be coming out both at the moment the button is pressed and at the moment exactly $ K $ seconds after the last press.

The input is given from Standard Input in the following format: > $ N $ $ K $ $ T $ $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $

Print the answer in a single line.

### Sample Explanation 1 If Takahashi presses the button at times $ 0,2,10,16 $ , hot water is always coming out from time $ 0 $ to time $ 20 $ . If he presses the button $ 3 $ times or fewer, it is impossible to keep hot water always coming out, so the answer is $ 4 $ . ### Constraints - $ 1 \leq N \leq 2 \times 10^5 $ - $ 1 \leq K \leq 10^9 $ - $ 1 \leq T \leq 10^9 $ - $ 0 \leq A_i \leq 10^9 $ - All input values are integers.