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: Accepted)

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

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

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

#define BIG 2000000007

#define MOD 1000000007
typedef uint64_t ull;
typedef  int64_t sll;

#define N_MAX 200000
#define M_MAX 30

typedef struct {
	int32_t a;
	int32_t b;
} hw;

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

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


typedef struct {
	ull s;
	ull t;
	int32_t 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;
size_t slen;
size_t tlen;
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];
ull c[N_MAX];
// char s[N_MAX + 1];
// char t[N_MAX + 1];
// 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 dq[N_MAX][M_MAX];
// hwll dp[N_MAX + 1][N_MAX + 1];
// struct_a dp[N_MAX + 1][N_MAX + 1];

// hw arr[N_MAX];
// hwll arr[N_MAX * 2];
// hw brr[M_MAX];
// linell arr[N_MAX];

// ull bitdp[1 << N_MAX];

// ull digitdp[10001][   2][  100];
//            pos  less  carry


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

void swap_adj (ull *a, ull *b) {
	if (*a != *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;
}

int32_t digits (ull x) {
	int32_t 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;
}

// int32_t nextroute (int32_t arr[]) {
// 	int32_t i = n - 1;
// 	int32_t 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(int32_t), comp);
// 	return 0;
// }

int32_t targetdig (ull x, int32_t index /* 1-indexed */) {
	// static...?
	int32_t posmax = digits(x);
	if (posmax < index) return -1;
	while (posmax > index) {
		posmax--;
		x /= 10;
	}
	return x % 10;
}

int32_t charcomp (const char left, const char right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int32_t pcharcomp (const char *left, const char *right) {
	return charcomp(*left, *right);
}

int32_t pcharrevcomp (const char *left, const char *right) {
	return charcomp(*right, *left);
}

int32_t intcomp (const int32_t left, const int32_t right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int32_t pintcomp (const int32_t *left, const int32_t *right) {
	return intcomp(*left, *right);
}

int32_t ullcomp (const ull left, const ull right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int32_t pullcomp (const ull *left, const ull *right) {
	return ullcomp(*left, *right);
}

int32_t sllcomp (const sll left, const sll right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int32_t psllcomp (const sll *left, const sll *right) {
	return sllcomp(*left, *right);
}

int32_t phwAcomp (const hw *left, const hw *right) {
	return intcomp(left->a, right->a);
}

int32_t phwBcomp (const hw *left, const hw *right) {
	return intcomp(left->b, right->b);
}

int32_t phwABcomp (const hw *left, const hw *right) {
	int32_t x = phwAcomp(left, right);
	if (x) return x;
	return phwBcomp(left, right);
}

int32_t phwllAcomp (const hwll *left, const hwll *right) {
	return sllcomp(left->a, right->a);
}

int32_t phwllBcomp (const hwll *left, const hwll *right) {
	return sllcomp(left->b, right->b);
}

int32_t phwllABcomp (const hwll *left, const hwll *right) {
	int32_t x = phwllAcomp(left, right);
	if (x) return x;
	return phwllBcomp(left, right);
}

int32_t pstrAcomp (const struct_a *left, const struct_a *right) {
	int32_t 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;
}

int32_t 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;
}

void printquotient (ull left, ull right) {
	const int32_t digits = 20;

	printf("%llu.", left / right);
	left %= right;
	for (int32_t i = 0; i < digits; i++) {
		left *= 10;
		printf("%1d", left / right);
		left %= right;
	}
	puts("");

	return;
}


bool isonedge (hwll x) {
	return (x.a == 0) || (x.a == h) || (x.b == 0) || (x.b == w);
}

ull converttoint (hwll x) {
	if (x.a == 0) {
		return w - x.b; // w ~ 0
	} else if (x.b == 0) {
		return w + x.a; // w ~ h+w
	} else if (x.a == h) {
		return (h + w) + x.b; // h+w ~ h+2w
	} else {
		return (h + w) * 2 - x.a; // (2h+2w) ~ (h+2w)
	}
}

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

	// if (k % 2 == 0) {
	// 	for (i = 0; i < n; i++) {
	// 		printf("%llu%c", ((i == 0) ? (k / 2 - 1) : (k / 2)), ((i == n - 1) ? '\n' : ' '));
	// 	}
	// } else {
	// 	//
	// }

	// ull p2, p3, p5;
	// p2 = p3 = p5 = 0;
	// while (n % 2) {
	// 	n /= 2;
	// 	p2++;
	// }
	// while (n % 3) {
	// 	n /= 3;
	// 	p3++;
	// }
	// while (n % 5) {
	// 	n /= 5;
	// 	p5++;
	// }
	// if (n > 1) goto fail;

	for (i = 0; i < n; i++) {
		dq[a[i]][c[i] - 1] ^= 1;
		dq[b[i]][c[i] - 1] ^= 1;
	}

	for (i = 0; i < n; i++) {
		if (dq[a[i]][c[i] - 1]) dp[a[i]]++;
		if (dq[b[i]][c[i] - 1]) dp[b[i] + 1]--;
	}

	ull timemax = 100005;
	for (i = 0; i <= timemax; i++) {
		sum += dp[i];
		if (result < sum) result = sum;
	}

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

	return 0;

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

	fail:
	// puts("NO");
	// puts("No");
	puts("0");
	return 1;
}

int32_t main (void) {
	int32_t i, j;
	int32_t x, y;

	// scanf("%llu%llu", &h, &w);
	scanf("%llu%llu", &n, &m);
	// scanf("%llu%llu", &k, &n);
	// scanf("%llu%llu", &vua, &vub, &vuc, &vud);
	// scanf("%s", s);
	// scanf("%s", t);
	// scanf("%lld%lld", &vsa, &vsb);
	// for (i = 0; i < n; i++) {
	// 	scanf("%llu", &a[i]);
	// }

	// for (i = 0; i < h; i++) {
	// 	scanf("%llu", &a[i]);
	// }
	// for (i = 0; i < w; i++) {
	// 	scanf("%llu", &b[i]);
	// }
	for (i = 0; i < n; i++) {
		scanf("%llu%llu%llu", &a[i], &b[i], &c[i]);
	}
	// for (i = 0; i < h; i++) {
	// 	for (j = 0; j < w; j++) {
	// 		scanf("%llu", &a[i][j]);
	// 	}
	// }

	solve();

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

	// while (scanf("%llu%llu", &n, &k), n + k) {
	// 	for (i = 0; i < n; i++) {
	// 		scanf("%llu", &a[i]);
	// 	}
	// 	solve();
	// }

	return 0;
}