The Pleasant Walk

There are n houses along the road where Anya lives, each one is painted in one of k possible colors.

Anya likes walking along this road, but she doesn't like when two adjacent houses at the road have the same color. She wants to select a long segment of the road such that no two adjacent houses have the same color.

Help Anya find the longest segment with this property.

Input

The first line contains two integers n and k — the number of houses and the number of colors (1 ≤ n ≤ 100 000, 1 ≤ k ≤ 100 000).

The next line contains n integers a_1, a_2, …, a_n — the colors of the houses along the road (1 ≤ a_i ≤ k).

Output

Output a single integer — the maximum number of houses on the road segment having no two adjacent houses of the same color.

Example

Input

8 3 1 2 3 3 2 1 2 2

Output

4

Note

In the example, the longest segment without neighboring houses of the same color is from the house 4 to the house 7. The colors of the houses are [3, 2, 1, 2] and its length is 4 houses.

inputFormat

Input

The first line contains two integers n and k — the number of houses and the number of colors (1 ≤ n ≤ 100 000, 1 ≤ k ≤ 100 000).

The next line contains n integers a_1, a_2, …, a_n — the colors of the houses along the road (1 ≤ a_i ≤ k).

outputFormat

Output

Output a single integer — the maximum number of houses on the road segment having no two adjacent houses of the same color.

Example

Input

8 3 1 2 3 3 2 1 2 2

Output

4

Note

In the example, the longest segment without neighboring houses of the same color is from the house 4 to the house 7. The colors of the houses are [3, 2, 1, 2] and its length is 4 houses.

样例

8 3
1 2 3 3 2 1 2 2

4