test

Posted 2021-12-08 mekakucityactor

B. Pairs

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Toad Ivan has mm pairs of integers, each integer is between 11 and nn, inclusive. The pairs are (a1,b1),(a2,b2),…,(am,bm)(a1,b1),(a2,b2),…,(am,bm).

He asks you to check if there exist two integers xx and yy (1≤x<y≤n1≤x<y≤n) such that in each given pair at least one integer is equal to xx or yy.

Input

The first line contains two space-separated integers nn and mm (2≤n≤3000002≤n≤300000, 1≤m≤3000001≤m≤300000) — the upper bound on the values of integers in the pairs, and the number of given pairs.

The next mm lines contain two integers each, the ii-th of them contains two space-separated integers aiai and bibi (1≤ai,bi≤n,ai≠bi1≤ai,bi≤n,ai≠bi) — the integers in the ii-th pair.

Output

Output "YES" if there exist two integers xx and yy (1≤x<y≤n1≤x<y≤n) such that in each given pair at least one integer is equal to xx or yy. Otherwise, print "NO". You can print each letter in any case (upper or lower).

Examples

input

Copy

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

output

Copy

NO

input

Copy

5 4
1 2
2 3
3 4
4 5

output

Copy

YES

input

Copy

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

output

Copy

YES

Note

In the first example, you can‘t choose any xx, yy 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=2x=2 and y=4y=4.

In the third example, you can choose x=1x=1 and y=2y=2.

题意：有m个数对(ai,bi)，问是否存在两个数x,y使每个数对至少有一个数字=x或者=y

题解：通过枚举第一个数对中的数字可以确定后面的数字。即如果a1=x，那么把所有不含a1的数对存起来，判断数对中数字最多的数量是否=不含a1的数的总个数，同理可以枚举b1=x。