Substring Comparison

AtCoder

IDarc165_d

Time2000ms

Memory256MB

Difficulty—

For an integer sequence $X=(X_1,X_2,\dots,X_n)$, let $X[L,R]$ denote the integer sequence $(X_L,X_{L+1},\dots,X_{R})$. You are given integers $N$ and $M$, and $M$ quadruples of integers $(A_i,B_i,C_i,D_i)$. Determine if there is an integer sequence $X$ of length $N$ that satisfies the following condition for every $i=1,2,\dots,M$: * $X[A_i,B_i]$ is lexicographically smaller than $X[C_i,D_i]$. What is lexicographical order on sequences?A sequence $S = (S_1,S_2,\ldots,S_{|S|})$ is **lexicographically smaller** than $T = (T_1,T_2,\ldots,T_{|T|})$ when 1. or 2. below holds. Here, $|S|$ and $|T|$ denotes the lengths of $S$ and $T$, respectively. 1. $|S| \lt |T|$ and $(S_1,S_2,\ldots,S_{|S|}) = (T_1,T_2,\ldots,T_{|S|})$. 2. There is an integer $1 \leq i \leq \min\lbrace |S|, |T| \rbrace$ that satisfy both of the following: * $(S_1,S_2,\ldots,S_{i-1}) = (T_1,T_2,\ldots,T_{i-1})$. * $S_i$ is smaller than $T_i$ (as a number). ## Constraints * $2 \leq N \leq 2000$ * $1 \leq M \leq 2000$ * $1 \leq A_i \leq B_i \leq N$ * $1 \leq C_i \leq D_i \leq N$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $C_1$ $D_1$ $A_2$ $B_2$ $C_2$ $D_2$ $\vdots$ $A_M$ $B_M$ $C_M$ $D_M$ [samples]

Samples

Input #1

4 2
1 3 3 4
4 4 1 2

Output #1

Yes

For example, $X=(1,1,2,1)$ satisfies the condition.

Input #2

3 2
1 2 2 3
2 2 1 1

Output #2

No

No integer sequence $X$ satisfies the condition.

Input #3

15 20
2 5 6 14
11 14 10 10
13 15 6 10
8 10 3 8
7 8 1 9
2 8 14 15
14 14 5 12
6 10 9 9
1 4 10 14
5 14 6 7
8 10 5 8
8 10 11 15
4 8 4 11
7 9 1 4
8 10 3 3
11 13 8 14
6 13 4 15
4 7 6 11
2 5 1 2
8 14 6 8

Output #3

No

API Response (JSON)

{
  "problem": {
    "name": "Substring Comparison",
    "description": {
      "content": "For an integer sequence $X=(X_1,X_2,\\dots,X_n)$, let $X[L,R]$ denote the integer sequence $(X_L,X_{L+1},\\dots,X_{R})$. You are given integers $N$ and $M$, and $M$ quadruples of integers $(A_i,B_i,C_i,",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc165_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "For an integer sequence $X=(X_1,X_2,\\dots,X_n)$, let $X[L,R]$ denote the integer sequence $(X_L,X_{L+1},\\dots,X_{R})$.\nYou are given integers $N$ and $M$, and $M$ quadruples of integers $(A_i,B_i,C_i,...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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