1169_B. Pairs
Toad Ivan has m pairs of integers, each integer is between 1 and n, inclusive. The pairs are (a_1, b_1), (a_2, b_2), …, (a_m, b_m). 

He asks you to check if there exist two integers x and y (1 ≤ x < y ≤ n) such that in each given pair at least one integer is equal to x or y.

Input

The first line contains two space-separated integers n and m (2 ≤ n ≤ 300 000, 1 ≤ m ≤ 300 000) — the upper bound on the values of integers in the pairs, and the number of given pairs.

The next m lines contain two integers each, the i-th of them contains two space-separated integers a_i and b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i) — the integers in the i-th pair.

Output

Output "YES" if there exist two integers x and y (1 ≤ x < y ≤ n) such that in each given pair at least one integer is equal to x or y. Otherwise, print "NO". You can print each letter in any case (upper or lower).

Examples

Input


4 6
1 2
1 3
1 4
2 3
2 4
3 4


Output


NO


Input


5 4
1 2
2 3
3 4
4 5


Output


YES


Input


300000 5
1 2
1 2
1 2
1 2
1 2


Output


YES

Note

In the first example, you can't choose any x, y because for each such pair you can find a given pair where both numbers are different from chosen integers.

In the second example, you can choose x=2 and y=4.

In the third example, you can choose x=1 and y=2.
```python
bound, m = [int(x) for x in input().split()]

if m == 1:
    print("YES")
    exit(0)

pairs_uniq = set()
for _ in range(m):
    x = [int(x) for x in input().split()]
    x.sort()
    pairs_uniq.add((x[0], x[1]))

if len(pairs_uniq) == 1:
    print("YES")
    exit(0)

pairs = [x for x in pairs_uniq]

# Choose the first one as our x
for x in pairs[0]:
    no_x_pairs = [n for n in pairs if n[0] != x and n[1] != x]

    x_pairs_count = 0
    d = {}
    for (i, j) in pairs:
        if i != x and j != x:
            if i not in d:
                d[i] = 0
            d[i] += 1
            if j not in d:
                d[j] = 0
            d[j] += 1
        else:
            x_pairs_count += 1

    max_ = 0 if len(d.values()) == 0 else sorted(d.values())[-1]
    if max_ + x_pairs_count == len(pairs):
        print("YES")
        exit(0)

print("NO")

```