FF

AtCoder
IDabc278_c
Time2000ms
Memory256MB
Difficulty—
Takahashi runs an SNS "Twidai," which has $N$ users from user $1$ through user $N$. In Twidai, users can follow or unfollow other users. $Q$ operations have been performed since Twidai was launched. The $i$\-th $(1\leq i\leq Q)$ operation is represented by three integers $T_i$, $A_i$, and $B_i$, whose meanings are as follows: * If $T_i = 1$: it means that user $A_i$ follows user $B_i$. If user $A_i$ is already following user $B_i$ at the time of this operation, it does not make any change. * If $T_i = 2$: it means that user $A_i$ unfollows user $B_i$. If user $A_i$ is not following user $B_i$ at the time of this operation, it does not make any change. * If $T_i = 3$: it means that you are asked to determine if users $A_i$ and $B_i$ are following each other. You need to print `Yes` if user $A_i$ is following user $B_i$ and user $B_i$ is following user $A_i$, and `No` otherwise. When the service was launched, no users were following any users. Print the correct answers for all operations such that $T_i = 3$ in ascending order of $i$. ## Constraints * $2 \leq N \leq 10 ^ 9$ * $1 \leq Q \leq 2\times10 ^ 5$ * $T _ i=1,2,3\ (1\leq i\leq Q)$ * $1 \leq A _ i \leq N\ (1\leq i\leq Q)$ * $1 \leq B _ i \leq N\ (1\leq i\leq Q)$ * $A _ i\neq B _ i\ (1\leq i\leq Q)$ * There exists $i\ (1\leq i\leq Q)$ such that $T _ i=3$. * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $Q$ $T _ 1$ $A _ 1$ $B _ 1$ $T _ 2$ $A _ 2$ $B _ 2$ $\vdots$ $T _ Q$ $A _ Q$ $B _ Q$ [samples]
Samples
Input #1
3 9
1 1 2
3 1 2
1 2 1
3 1 2
1 2 3
1 3 2
3 1 3
2 1 2
3 1 2
Output #1
No
Yes
No
No

Twidai has three users. The nine operations are as follows.

*   User $1$ follows user $2$. No other users are following or followed by any users.
*   Determine if users $1$ and $2$ are following each other. User $1$ is following user $2$, but user $2$ is not following user $1$, so `No` is the correct answer to this operation.
*   User $2$ follows user $1$.
*   Determine if users $1$ and $2$ are following each other. User $1$ is following user $2$, and user $2$ is following user $1$, so `Yes` is the correct answer to this operation.
*   User $2$ follows user $3$.
*   User $3$ follows user $2$.
*   Determine if users $1$ and $3$ are following each other. User $1$ is not following user $3$, and user $3$ is not following user $1$, so `No` is the correct answer to this operation.
*   User $1$ unfollows user $2$.
*   Determine if users $1$ and $2$ are following each other. User $2$ is following user $1$, but user $1$ is not following user $2$, so `No` is the correct answer to this operation.
Input #2
2 8
1 1 2
1 2 1
3 1 2
1 1 2
1 1 2
1 1 2
2 1 2
3 1 2
Output #2
Yes
No

A user may follow the same user multiple times.
Input #3
10 30
3 1 6
3 5 4
1 6 1
3 1 7
3 8 4
1 1 6
2 4 3
1 6 5
1 5 6
1 1 8
1 8 1
2 3 10
1 7 6
3 5 6
1 6 7
3 6 7
1 9 5
3 8 6
3 3 8
2 6 9
1 7 1
3 10 8
2 9 2
1 10 9
2 6 10
2 6 8
3 1 6
3 1 8
2 8 5
1 9 10
Output #3
No
No
No
No
Yes
Yes
No
No
No
Yes
Yes
API Response (JSON) 
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  "problem": {
    "name": "FF",
    "description": {
      "content": "Takahashi runs an SNS \"Twidai,\" which has $N$ users from user $1$ through user $N$. In Twidai, users can follow or unfollow other users. $Q$ operations have been performed since Twidai was launched. T",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc278_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi runs an SNS \"Twidai,\" which has $N$ users from user $1$ through user $N$. In Twidai, users can follow or unfollow other users.\n$Q$ operations have been performed since Twidai was launched. T...",
      "is_translate": false,
      "language": "English"
    }
  ]
}
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