Problem:
Score : 400 points

Problem Statement

On a planet far, far away, M languages are spoken. They are conveniently numbered 1 through M.

For CODE FESTIVAL 20XX held on this planet, N participants gathered from all over the planet.

The i-th (1≦i≦N) participant can speak K_i languages numbered L_{i,1}, L_{i,2}, ..., L_{i,{}K_i}.

Two participants A and B can communicate with each other if and only if one of the following conditions is satisfied:

There exists a language that both A and B can speak.

There exists a participant X that both A and B can communicate with.

Determine whether all N participants can communicate with all other participants.

Constraints

2≦N≦10^5

1≦M≦10^5

1≦K_i≦M

(The sum of all K_i)≦10^5

1≦L_{i,j}≦M

L_{i,1}, L_{i,2}, ..., L_{i,{}K_i} are pairwise distinct.

Partial Score

200 points will be awarded for passing the test set satisfying the following: N≦1000, M≦1000 and (The sum of all K_i)≦1000.

Additional 200 points will be awarded for passing the test set without additional constraints.

Input

The input is given from Standard Input in the following format:

N M
K_1 L_{1,1} L_{1,2} ... L_{1,{}K_1}
K_2 L_{2,1} L_{2,2} ... L_{2,{}K_2}
:
K_N L_{N,1} L_{N,2} ... L_{N,{}K_N}

Output

If all N participants can communicate with all other participants, print YES. Otherwise, print NO.

Sample Input 1

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

Sample Output 1

YES

Any two participants can communicate with each other, as follows:

Participants 1 and 2: both can speak language 2.

Participants 2 and 3: both can speak language 4.

Participants 1 and 3: both can communicate with participant 2.

Participants 3 and 4: both can speak language 6.

Participants 2 and 4: both can communicate with participant 3.

Participants 1 and 4: both can communicate with participant 2.

Note that there can be languages spoken by no participant.

Sample Input 2

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

Sample Output 2

NO

For example, participants 1 and 3 cannot communicate with each other.

Solution in Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

const (
	initialBufSize = 100000
	maxBufSize     = 10000000
)

var (
	sc = bufio.NewScanner(os.Stdin)
	wt = bufio.NewWriter(os.Stdout)
)

func next() string {
	sc.Scan()
	return sc.Text()
}

func nextInt() int {
	i, _ := strconv.Atoi(next())
	return i
}

func puts(a ...interface{}) {
	fmt.Fprintln(wt, a...)
}

type UnionFind struct {
	Par []int
}

func NewUnionFind(n int) *UnionFind {
	uf := &UnionFind{
		Par: make([]int, n),
	}
	uf.Init(n)
	return uf
}

func (uf *UnionFind) Init(n int) {
	for i := 0; i < n; i++ {
		uf.Par[i] = -1
	}
}

func (uf *UnionFind) Find(x int) int {
	if uf.Par[x] < 0 {
		return x
	}
	uf.Par[x] = uf.Find(uf.Par[x])
	return uf.Par[x]
}

func (uf *UnionFind) Unite(x, y int) {
	x, y = uf.Find(x), uf.Find(y)
	if x == y {
		return
	}

	if uf.Par[x] > uf.Par[y] {
		x, y = y, x
	}
	uf.Par[x] += uf.Par[y]
	uf.Par[y] = x
}

func (uf *UnionFind) Same(x, y int) bool {
	return uf.Find(x) == uf.Find(y)
}

// xの属する集合の要素数
func (uf *UnionFind) Size(x int) int {
	return -uf.Par[uf.Find(x)]
}

func main() {
	sc.Split(bufio.ScanWords)
	sc.Buffer(make([]byte, initialBufSize), maxBufSize)
	defer wt.Flush()

	n, m := nextInt(), nextInt()
	// 各言語の話者リスト
	speaker := make([][]int, m)
	for i := range speaker {
		speaker[i] = make([]int, 0)
	}
	for i := 0; i < n; i++ {
		k := nextInt()
		for j := 0; j < k; j++ {
			l := nextInt() - 1
			speaker[l] = append(speaker[l], i)
		}
	}

	uf := NewUnionFind(n)
	for _, sp := range speaker {
		if len(sp) == 0 {
			continue
		}
		for i := 1; i < len(sp); i++ {
			uf.Unite(sp[0], sp[i])
		}
	}

	if uf.Size(0) == n {
		puts("YES")
	} else {
		puts("NO")
	}
}