Problem:
Score : 400 points

Problem Statement

Joisino is planning to record N TV programs with recorders.

The TV can receive C channels numbered 1 through C.

The i-th program that she wants to record will be broadcast from time s_i to time t_i (including time s_i but not t_i) on Channel c_i.

Here, there will never be more than one program that are broadcast on the same channel at the same time.

When the recorder is recording a channel from time S to time T (including time S but not T), it cannot record other channels from time S-0.5 to time T (including time S-0.5 but not T).

Find the minimum number of recorders required to record the channels so that all the N programs are completely recorded.

Constraints

1≤N≤10^5

1≤C≤30

1≤s_i<t_i≤10^5

1≤c_i≤C

If c_i=c_j and i≠j, either t_i≤s_j or s_i≥t_j.

All input values are integers.

Input

Input is given from Standard Input in the following format:

N C
s_1 t_1 c_1
:
s_N t_N c_N

Output

When the minimum required number of recorders is x, print the value of x.

Sample Input 1

3 2
1 7 2
7 8 1
8 12 1

Sample Output 1

2

Two recorders can record all the programs, for example, as follows:

With the first recorder, record Channel 2 from time 1 to time 7. The first program will be recorded. Note that this recorder will be unable to record other channels from time 0.5 to time 7.

With the second recorder, record Channel 1 from time 7 to time 12. The second and third programs will be recorded. Note that this recorder will be unable to record other channels from time 6.5 to time 12.

Sample Input 2

3 4
1 3 2
3 4 4
1 4 3

Sample Output 2

3

There may be a channel where there is no program to record.

Sample Input 3

9 4
56 60 4
33 37 2
89 90 3
32 43 1
67 68 3
49 51 3
31 32 3
70 71 1
11 12 3

Sample Output 3

2

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

/*
cat <<EOF >mistaken-paste
*/

#pragma GCC diagnostic ignored "-Wincompatible-pointer-types"

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>

#define BIG 2000000007

#define MOD 1000000007
typedef unsigned long long ull;
typedef   signed long long sll;

#define N_MAX 100000
#define M_MAX 200

typedef struct {
	int a;
	int b;
} hw;

typedef struct {
	sll a;
	sll b;
} hwll;


typedef struct {
	ull s;
	ull t;
	int c;
} struct_a;



const hw vector8[8] = {
	{-1, -1},
	{-1,  0},
	{-1, +1},
	{ 0, -1},
	{ 0, +1},
	{+1, -1},
	{+1,  0},
	{+1, +1}
};

ull n, m;
ull h, w;
ull k;
ull vua, vub, vuc, vud, vue, vuf;
sll vsa, vsb, vsc, vsd, vse, vsf;
long double vra, vrb, vrc;
// ull a[N_MAX];
// sll a[N_MAX];
// ull a[N_MAX][N_MAX];
// ull wall[N_MAX][M_MAX];
// ull b[N_MAX];
// sll b[N_MAX];
// ull b[N_MAX][N_MAX];
// sll b[N_MAX][N_MAX];
// char s[N_MAX + 1];
// char t[N_MAX + 1];
// size_t slen;
// size_t tlen;
// char s[N_MAX][M_MAX + 1];

// ull dp[N_MAX];
// sll dp[N_MAX];
bool dp[N_MAX];
// ull dq[N_MAX];
// ull dp[N_MAX + 1][N_MAX + 1];
// ull dp[N_MAX][M_MAX + 1];

// hw arr[N_MAX];
// hwll arr[N_MAX];
// hw brr[M_MAX];

// ull digitdp[102][   2][    2];
//          pos  less  carry


struct_a arr[N_MAX * 2];
// struct_b brr[N_MAX * 2];

void swap_adj (ull *a, ull *b) {
	ull tmp = *b;
	*b = *a;
	*a = tmp;
	return;
}

ull divide (ull a, ull b) {
	ull x = MOD - 2;
	ull ans = 1;
	while (x) {
		if (x & 1) ans = (ans * b) % MOD;
		b = (b * b) % MOD;
		x /= 2;
	}
	return (a * ans) % MOD;
}

int digits (ull x) {
	int i = 1;
	while (x >= 10) {
		x /= 10;
		i++;
	}
	return i;
}

ull umin (ull x, ull y) {
	return (x < y) ? x : y;
}

ull umax (ull x, ull y) {
	return (x > y) ? x : y;
}

sll smin (sll x, sll y) {
	return (x < y) ? x : y;
}

sll smax (sll x, sll y) {
	return (x > y) ? x : y;
}

ull gcd (ull x, ull y) {
	if (x < y) {
		return gcd(y, x);
	} else if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}

ull bitpow (ull a, ull x, ull modulo) {
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= modulo;
		}
		x /= 2;
		a = (a * a) % modulo;
	}
	return result;
}

// int nextroute (int arr[]) {
// 	int i = n - 1;
// 	int j, x;
// 	while (arr[i - 1] > arr[i]) i--;

// 	x = n;
// 	for (j = i; j < n; j++) {
// 		if (arr[j] < arr[i - 1]) continue;
// 		if (x == n || arr[x] > arr[j]) x = j;
// 	}
// 	arr[i - 1] ^= arr[x];
// 	arr[x] ^= arr[i - 1];
// 	arr[i - 1] ^= arr[x];

// 	qsort(&arr[i], n - i, sizeof(int), comp);
// 	return 0;
// }

int targetdig (ull x, int index /* 1-indexed */) {
	// static...?
	int posmax = digits(x);
	if (posmax < index) return -1;
	while (posmax > index) {
		posmax--;
		x /= 10;
	}
	return x % 10;
}

int charcomp (const char left, const char right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int pcharcomp (const char *left, const char *right) {
	return charcomp(*left, *right);
}

int intcomp (const int left, const int right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int pintcomp (const int *left, const int *right) {
	return intcomp(*left, *right);
}

int ullcomp (const ull left, const ull right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int pullcomp (const ull *left, const ull *right) {
	return ullcomp(*left, *right);
}

int sllcomp (const sll left, const sll right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int psllcomp (const sll *left, const sll *right) {
	return sllcomp(*left, *right);
}

int phwAcomp (const hw *left, const hw *right) {
	return intcomp(left->a, right->a);
}

int phwBcomp (const hw *left, const hw *right) {
	return intcomp(left->b, right->b);
}

int phwABcomp (const hw *left, const hw *right) {
	int x = phwAcomp(left, right);
	if (x) return x;
	return phwBcomp(left, right);
}

int phwllAcomp (const hwll *left, const hwll *right) {
	return sllcomp(left->a, right->a);
}

int phwllBcomp (const hwll *left, const hwll *right) {
	return sllcomp(left->b, right->b);
}

int phwllABcomp (const hwll *left, const hwll *right) {
	int x = phwllAcomp(left, right);
	if (x) return x;
	return phwllBcomp(left, right);
}

int pstrAcomp (const struct_a *left, const struct_a *right) {
	int x;
	if (x = ullcomp(left->t, right->t)) return x;
	if (x = ullcomp(left->s, right->s)) return x;
	if (x = intcomp(left->c, right->c)) return x;
	return 0;
}

int bitlet (char c) {
	return (1 << (c - 'a'));
}

ull ullabs (ull a, ull b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll sllabs (sll a, sll b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll nibutanlobo (bool (*func)(sll arg), sll ok, sll ng) {
	while (sllabs(ok, ng) > 1) {
		sll med = (ok + ng) / 2;
		if (func(med)) {
			ok = med;
		} else {
			ng = med;
		}

		// printf("debug: [%lld %lld)\n", ok, ng);
	}

	if (!func(ok)) return ok * 2 - ng;
	return ok;
}


ull filled[N_MAX];

ull solve () {
	sll i, j, ki;
	ull result = 0;
	// sll result;
	ull sum = 0;
	// qsortの際には"p"ullcompを使う


	qsort(arr, n, sizeof(struct_a), pstrAcomp);
	for (i = 0; i < n; i++) {
		dp[i] = false;
	}
	sum = n;

	while (sum) {
		for (i = 0; i < m; i++) {
			filled[i] = 0;
		}

		result++;

		for (i = 0; i < n; i++) {
			if (dp[i]) continue;

			if (arr[i].s <= filled[arr[i].c]) continue;

			dp[i] = true;
			sum--;

			for (j = 0; j < m; j++) {
				if (j == arr[i].c) continue;

				filled[j] = umax(filled[j], arr[i].t);
			}
		}
	}

	printf("%lld\n", result);
	// puts(s);

	return 0;

	success:
	puts("Yes");
	// printf("%llu\n", result);
	return 0;

	fail:
	puts("No");
	return 1;
}

int main (void) {
	int i, j;
	int x, y;

	// scanf("%llu%llu", &h, &w);
	scanf("%llu%llu", &n, &m);
	// scanf("%llu%llu", &vua, &vub);
	// scanf("%s", s);
	// slen = strlen(s);
	// scanf("%s", t);
	// tlen = strlen(t);
	// for (i = 0; i < n; i++) {
	// 	scanf("%llu", &a[i]);
	// }
	// for (i = 0; i < m; i++) {
	// 	scanf("%lld", &b[i]);
	// }
	for (i = 0; i < n; i++) {
		scanf("%llu%llu%d", &arr[i].s, &arr[i].t, &arr[i].c);
		arr[i].c--;
	}

	solve();

	// for (i = 0; i < n; i++) {
	// 	// scanf("%llu%llu", &vua, &vub);
	// 	scanf("%s", s);
	// 	solve();
	// }

	return 0;
}