You have a device for working with permutations $$$p_1, p_2, \ldots, p_n$$$ of integers from $$$1$$$ to $$$n$$$. It can perform $$$m$$$ operations. $$$i$$$-th operation is described by two integers $$$a_i, b_i$$$ $$$(1 \le a_i, b_i \le n, a_i \neq b_i)$$$. If you apply it, it will do the following: if $$$p_{a_i} \gt p_{b_i}$$$, then the device will swap $$$p_{a_i}, p_{b_i}$$$. Otherwise, it will do nothing.
You can apply these operations any number of times, in any order (you can use one operation more than once).
You are interested in whether you can use this device to get every permutation from every other permutation. In other words, determine whether for every two permutations $$$p_1, p_2, \ldots, p_n$$$ and $$$q_1, q_2, \ldots, q_n$$$ of the integers from $$$1$$$ to $$$n$$$, there exists a sequence of operations that can be applied to $$$p$$$ to obtain $$$q$$$.
Recall that the permutation of integers from $$$1$$$ to $$$n$$$ is an array of length $$$n$$$ containing each integer from $$$1$$$ to $$$n$$$ exactly once.
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The description of test cases follows.
The first line of each test case contains two integers $$$n, m$$$ ($$$1 \le n \le 2 \cdot 10^5, 0 \le m \le 2 \cdot 10^5$$$) —the length of permutations your device can handle and the number of operations it can perform.
The $$$i$$$-th of the $$$m$$$ following lines contains two integers $$$a_i, b_i$$$ $$$(1 \le a_i, b_i \le n, a_i \neq b_i)$$$ describing the $$$i$$$-th operation: if $$$p_{a_i} \gt p_{b_i}$$$, the device can swap the elements $$$p_{a_i}, p_{b_i}$$$ of the permutation.
It is guaranteed that all pairs $$$(a_i, b_i)$$$ are pairwise distinct, but note that pairs $$$(x, y)$$$ and $$$(y, x)$$$ may occur simultaneously for some $$$x, y$$$.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$, and the sum of $$$m$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
For each test case, print YES if you can obtain any permutation from any other permutation with this device, and NO otherwise.
You can print YES and NO in any case (e.g. the strings yEs, yes, Yes will be taken as a positive answer).
52 11 23 41 22 11 33 15 41 22 33 44 55 63 55 11 24 32 44 14 63 12 32 13 21 21 3
NO YES NO YES NO
In the first example, we can swap $$$p_1$$$ and $$$p_2$$$ if $$$p_1 \gt p_2$$$. Thus, we can get the permutation $$$(2, 1)$$$ from the permutation $$$(1, 2)$$$, but we cannot get the permutation $$$(1, 2)$$$ from the permutation $$$(2, 1)$$$, so the answer is NO.
In the second example, we can swap $$$p_1, p_2$$$ regardless of which one is larger (because we have both swap operations: with $$$a_i = 1, b_i = 2$$$ and with $$$a_i = 2, b_i = 1$$$). Also, we can swap $$$p_1, p_3$$$ regardless of which of them is greater. It is easy to show that in this case we can get from any permutation any other permutation, so the answer is YES.
