 2018 Asia Singapore Preliminary Contest #### Start

2018-09-14 18:00 AKDT

## 2018 Asia Singapore Preliminary Contest

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2018-09-14 23:00 AKDT
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# Problem BSwap to Sort

You are given an array $A[1...N]$ with integers in decreasing order and a list of pairs $(a_1, b_1)$, $(a_2, b_2),$ $\ldots$, $(a_ K, b_ K)$. You wish to sort the array $A$ in increasing order, each turn you choose an $i$ ($i$ can be chosen multiple times) and swap $A[a_ i]$ with $A[b_ i]$. Determine whether this is possible.

## Input

The first line contains two integers, representing $N$ and $K$ respectively ($1 \leq N, K \leq 10^6$). The following $K$ lines each contains two integers, representing $a_ i$ and $b_ i$ respectively ($1 \leq a_ i < b_ i \leq N$).

## Output

Output “Yes” if it is possible to sort the array in increasing order, “No” otherwise.

Sample Input 1 Sample Output 1
5 2
1 5
2 4

Yes


Sample Input 2 Sample Output 2
5 4
1 4
2 3
4 5
1 5

No