human
Bear Limak examines a social network. Its main functionality is that two members can become friends (then they can talk with each other and share funny pictures).

There are n members, numbered 1 through n. m pairs of members are friends. Of course, a member can't be a friend with themselves.

Let A-B denote that members A and B are friends. Limak thinks that a network is reasonable if and only if the following condition is satisfied: For every three distinct members (X, Y, Z), if X-Y and Y-Z then also X-Z.

For example: if Alan and Bob are friends, and Bob and Ciri are friends, then Alan and Ciri should be friends as well.

Can you help Limak and check if the network is reasonable? Print "YES" or "NO" accordingly, without the quotes.

Input

The first line of the input contain two integers n and m (3 ≤ n ≤ 150 000, ) — the number of members and the number of pairs of members that are friends.

The i-th of the next m lines contains two distinct integers ai and bi (1 ≤ ai, bi ≤ n, ai ≠ bi). Members ai and bi are friends with each other. No pair of members will appear more than once in the input.

Output

If the given network is reasonable, print "YES" in a single line (without the quotes). Otherwise, print "NO" in a single line (without the quotes).

Examples

Input

4 3
1 3
3 4
1 4

Output

YES

Input

4 4
3 1
2 3
3 4
1 2

Output

NO

Input

10 4
4 3
5 10
8 9
1 2

Output

YES

Input

3 2
1 2
2 3

Output

NO

Note

The drawings below show the situation in the first sample (on the left) and in the second sample (on the right). Each edge represents two members that are friends. The answer is "NO" in the second sample because members (2, 3) are friends and members (3, 4) are friends, while members (2, 4) are not.

The above is tricky. Write me a correct solution in PYTHON3.
assistant
#Here is Python code to print "YES" or "NO" accordingly, without the quotes.

class CodeforcesTask771ASolution:
    def __init__(self):
        self.result = ''
        self.n_m = []
        self.edges = []

    def read_input(self):
        self.n_m = [int(x) for x in input().split(" ")]
        for x in range(self.n_m[1]):
            self.edges.append([int(y) for y in input().split(" ")])

    def process_task(self):
        graph = [[] for x in range(self.n_m[0])]
        lens = [0] * self.n_m[0]
        for edge in self.edges:
            graph[edge[0] - 1].append(edge[1])
            graph[edge[1] - 1].append(edge[0])
            lens[edge[0] - 1] += 1
            lens[edge[1] - 1] += 1
        component = [0] * self.n_m[0]
        comp_cnt = 0
        can = True
        fixed = set()
        for x in range(self.n_m[0]):
            if not component[x] or self.n_m[0] < 1000:
                if not component[x]:
                    comp_cnt += 1
                    component[x] = comp_cnt
                #print(component, x, graph[x], comp_cnt)
                for y in graph[x]:
                    if lens[y - 1] != lens[x]:
                        #print("x")
                        can = False
                        break
                    elif component[y - 1]:
                        if component[y - 1] != component[x]:
                            #print("d", component)
                            can = False
                            break
                    else:
                        if comp_cnt in fixed:
                            can = False
                            break
                        component[y - 1] = comp_cnt
                if not can:
                    break
                fixed.add(comp_cnt)
        self.result = "YES" if can else "NO"

    def get_result(self):
        return self.result

if __name__ == "__main__":
    Solution = CodeforcesTask771ASolution()
    Solution.read_input()
    Solution.process_task()
    print(Solution.get_result())