The legendary Farmer John is throwing a huge party, and animals from all over the world are hanging out at his house. His guests are hungry, so he instructs his cow Bessie to bring out the snacks! Moo!

There are $n$ snacks flavors, numbered with integers $1, 2, \ldots, n$. Bessie has $n$ snacks, one snack of each flavor. Every guest has exactly two favorite flavors. The procedure for eating snacks will go as follows:  First, Bessie will line up the guests in some way.  Then in this order, guests will approach the snacks one by one.  Each guest in their turn will eat all remaining snacks of their favorite flavor. In case no favorite flavors are present when a guest goes up, they become very sad.  

Help Bessie to minimize the number of sad guests by lining the guests in an optimal way.


-----Input-----

The first line contains integers $n$ and $k$ ($2 \le n \le 10^5$, $1 \le k \le 10^5$), the number of snacks and the number of guests. 

The $i$-th of the following $k$ lines contains two integers $x_i$ and $y_i$ ($1 \le x_i, y_i \le n$, $x_i \ne y_i$), favorite snack flavors of the $i$-th guest.


-----Output-----

Output one integer, the smallest possible number of sad guests.


-----Examples-----
Input
5 4
1 2
4 3
1 4
3 4

Output
1

Input
6 5
2 3
2 1
3 4
6 5
4 5

Output
0



-----Note-----

In the first example, Bessie can order the guests like this: $3, 1, 2, 4$. Guest $3$ goes first and eats snacks $1$ and $4$. Then the guest $1$ goes and eats the snack $2$ only, because the snack $1$ has already been eaten. Similarly, the guest $2$ goes up and eats the snack $3$ only. All the snacks are gone, so the guest $4$ will be sad. 

In the second example, one optimal ordering is $2, 1, 3, 5, 4$. All the guests will be satisfied.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'class UnionFind:\n    def __init__(self, n):\n        self.par = [i for i in range(n)]\n        self.size = [1] * n\n        self.edge = [0] * n\n        self.rank = [0] * n\n\n    def find(self, x):\n        if self.par[x] == x:\n            return x\n        else:\n            self.par[x] = self.find(self.par[x])\n            return self.par[x]\n\n    def same_check(self, x, y):\n        return self.find(x) == self.find(y)\n\n    def get_size(self, x):\n        return self.size[self.find(x)]\n\n    def union(self, x, y):\n        x = self.find(x)\n        y = self.find(y)\n        if x == y:\n            self.edge[x] += 1\n            return\n\n        if self.rank[x] < self.rank[y]:\n            self.par[x] = y\n            self.size[y] += self.size[x]\n            self.edge[y] += self.edge[x] + 1\n        else:\n            self.par[y] = x\n            self.size[x] += self.size[y]\n            self.edge[x] += self.edge[y] + 1\n            if self.rank[x] == self.rank[y]:\n                self.rank[x] += 1\n    \nn, k = [int(item) for item in input().split()]\nUF = UnionFind(2 * 10**5)\nfor i in range(k):\n    a, b = [int(item) for item in input().split()]\n    a -= 1; b -= 1\n    UF.union(a, b)\nseen = [False] * (2 * 10**5)\nans = 0\nfor i in range(2 * 10**5):\n    par = UF.find(i)\n    if seen[par]:\n        continue\n    if UF.edge[par] == 0:\n        continue\n    else:\n        ans += UF.edge[par] - (UF.size[par] - 1)\n    seen[par] = True \nprint(ans)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14426475