Islands
The island nation of Isola is made up of n islands. To facilitate travel between some of these islands, bridges have been constructed. To manage traffic effectively, no island is connected by more than two bridges. Each bridge allows travel in both directions. To fund the maintenance of these bridges and roads, the Isola government has implemented a toll of one unit for each bridge crossing.
Until recently, Isola had no bus service. In response to urgent demand, the first bus company, "Correira," was established. The company decided to set up bus routes between every pair of islands. However, if no bridge path exists between two islands, no route will be established between them.
Each route will have two trips per day: one in each direction. Naturally, buses will always take the least expensive route. "Correira" is keen to know the total number of units spent daily on bridge tolls for these bus crossings. Since Isola lacks programmers, the company seeks your help to solve this problem.
Input
The first line contains two integers n and m (1 ≤ n ≤ 100000; 0 ≤ m ≤ n) — representing the number of islands and bridges in Isola. The following m lines describe the bridges. Each line contains two integers x and y (1 ≤ x, y ≤ n; x ≠ y) — indicating the islands connected by a bridge. It is guaranteed that no island is connected by more than two bridges.
Output
Output a single integer — the total number of units required for the bus service operations.