Bacteria Coexistence (bioHazard)

The samples are arranged by number from 1 to n. The two samples of any conflicting pair cannot both appear in a range, and direction does not matter for a conflict. Count the valid non-empty contiguous ranges; the samples cannot be reordered. Duplicate conflicts are not subtracted twice.

输入格式

The first line contains n m, followed by m lines each with a b, denoting a conflicting pair. This site uses 1≤n≤200000, 0≤m≤200000, 1≤a,b≤n, and a≠b; duplicates and reversed duplicates are allowed.

输出格式

The number of valid ranges, as a 64-bit integer.

样例 1

输入：

3 3
2 3
1 3
3 1

输出：

4

样例 2

输入：

4 0

输出：

10

样例 3

输入：

4 3
1 4
4 1
2 3

输出：

6

样例说明

In Example 1, the valid ranges are the three single points and [1,2], for 4 in total. In Example 2, all 10 ranges are valid. In Example 3, the duplicated reversed relation counts as one, and there are 6 valid ranges in total.