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 (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bytes"
	"fmt"
	"io"
	"os"
	"strings"
)

func main() {
	if true {
		test()
	} else {
		solve(os.Stdin, os.Stdout)
	}
}

func solve(r io.Reader, w io.Writer) {
	var n int // number of participants
	var m int // number of languages
	fmt.Fscanln(r, &n, &m)
	// planet: paticipant -> lang -> bool
	planet := make(map[int]map[int]bool)
	for i := 0; i < n; i++ {
		planet[i] = make(map[int]bool)
		var langs int
		fmt.Fscan(r, &langs)
		for j := 0; j < langs; j++ {
			var lang int
			fmt.Fscan(r, &lang)
			planet[i][lang] = true
		}
	}

	if communicatable(planet, n) {
		fmt.Fprintln(w, "YES")
	} else {
		fmt.Fprintln(w, "NO")
	}
}

func communicatable(planet map[int]map[int]bool, n int) bool {
	// p1 -> p2 -> bool
	table := make(map[int]map[int]bool)
	for i := 0; i < n; i++ {
		table[i] = make(map[int]bool)
	}

	for p1, langs1 := range planet {
	P:
		for p2, langs2 := range planet {
			if !(p1 < p2) {
				continue P
			}
			for l2 := range langs2 {
				if _, ok := langs1[l2]; ok {
					table[p1][p2] = true
					table[p2][p1] = true
				}
			}
		}
	}

	seen := make(map[int]bool)
	traverse(table, 0, seen)
	for i := 0; i < n; i++ {
		if _, ok := seen[i]; !ok {
			return false
		}
	}
	return true
}

func traverse(g map[int]map[int]bool, i int, seen map[int]bool) {
	if _, ok := seen[i]; ok {
		return
	}
	seen[i] = true
	for v := range g[i] {
		traverse(g, v, seen)
	}
}

func canCommunicateWithX(planet map[int]map[int]bool, table map[int]map[int]bool) (bool, int) {
	newtable := make(map[int]map[int]bool)
	for i := 0; i < len(table); i++ {
		newtable[i] = make(map[int]bool)
	}
	new := 0
	end := true
	for p1 := range planet {
	P:
		for p2 := range planet {
			if !(p1 < p2) {
				continue P
			}
			if _, ok := table[p1][p2]; ok {
				continue P
			}
			for px1 := range table[p1] {
				if _, ok := table[p2][px1]; ok {
					new++
					newtable[p1][p2] = true
					continue P
				}
			}
			for px2 := range table[p2] {
				if _, ok := table[p1][px2]; ok {
					new++
					newtable[p1][p2] = true
					continue P
				}
			}
			end = false
		}
	}
	// update table
	for p1, ps := range newtable {
		for p2 := range ps {
			table[p1][p2] = true
			table[p2][p1] = true
		}
	}
	return end, new
}

func genRange(i, j int) []int {
	rs := make([]int, 0, j-i)
	for ; i < j; i++ {
		rs = append(rs, i)
	}
	return rs
}

func test() {
	tests := []struct {
		in   string
		want string
	}{
		{
			in: `4 6
3 1 2 3
2 4 2
2 4 6
1 6`,
			want: `YES
`,
		},
		{
			in: `4 4
2 1 2
2 1 2
1 3
2 4 3`,
			want: `NO
`,
		},
	}
	for i, tt := range tests {
		fmt.Printf("=== TEST %d\n", i)
		buf := new(bytes.Buffer)
		solve(strings.NewReader(tt.in), buf)
		if got := buf.String(); got != tt.want {
			fmt.Printf("%d: got %v, want %v\n", i, got, tt.want)
		}
	}
}