1401_E. Divide Square
There is a square of size 10^6 × 10^6 on the coordinate plane with four points (0, 0), (0, 10^6), (10^6, 0), and (10^6, 10^6) as its vertices.

You are going to draw segments on the plane. All segments are either horizontal or vertical and intersect with at least one side of the square.

Now you are wondering how many pieces this square divides into after drawing all segments. Write a program calculating the number of pieces of the square.

Input

The first line contains two integers n and m (0 ≤ n, m ≤ 10^5) — the number of horizontal segments and the number of vertical segments.

The next n lines contain descriptions of the horizontal segments. The i-th line contains three integers y_i, lx_i and rx_i (0 < y_i < 10^6; 0 ≤ lx_i < rx_i ≤ 10^6), which means the segment connects (lx_i, y_i) and (rx_i, y_i).

The next m lines contain descriptions of the vertical segments. The i-th line contains three integers x_i, ly_i and ry_i (0 < x_i < 10^6; 0 ≤ ly_i < ry_i ≤ 10^6), which means the segment connects (x_i, ly_i) and (x_i, ry_i).

It's guaranteed that there are no two segments on the same line, and each segment intersects with at least one of square's sides.

Output

Print the number of pieces the square is divided into after drawing all the segments.

Example

Input


3 3
2 3 1000000
4 0 4
3 0 1000000
4 0 1
2 0 5
3 1 1000000


Output


7

Note

The sample is like this:

<image>
```python
import sys, math
import io, os
data = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
#from bisect import bisect_left as bl, bisect_right as br, insort
#from heapq import heapify, heappush, heappop
#from collections import defaultdict as dd, deque, Counter
#from itertools import permutations,combinations
#def data(): return sys.stdin.readline().strip()
def mdata(): return list(map(int, data().split()))
def outl(var) : sys.stdout.write(' '.join(map(str, var))+'\n')
def out(var) : sys.stdout.write(str(var)+'\n')
from decimal import Decimal
#from fractions import Fraction
#sys.setrecursionlimit(100000)
INF = float('inf')
mod = int(1e9)+7

class SortedList:
    def __init__(self, iterable=[], _load=200):
        """Initialize sorted list instance."""
        values = sorted(iterable)
        self._len = _len = len(values)
        self._load = _load
        self._lists = _lists = [values[i:i + _load] for i in range(0, _len, _load)]
        self._list_lens = [len(_list) for _list in _lists]
        self._mins = [_list[0] for _list in _lists]
        self._fen_tree = []
        self._rebuild = True

    def _fen_build(self):
        """Build a fenwick tree instance."""
        self._fen_tree[:] = self._list_lens
        _fen_tree = self._fen_tree
        for i in range(len(_fen_tree)):
            if i | i + 1 < len(_fen_tree):
                _fen_tree[i | i + 1] += _fen_tree[i]
        self._rebuild = False

    def _fen_update(self, index, value):
        """Update `fen_tree[index] += value`."""
        if not self._rebuild:
            _fen_tree = self._fen_tree
            while index < len(_fen_tree):
                _fen_tree[index] += value
                index |= index + 1

    def _fen_query(self, end):
        """Return `sum(_fen_tree[:end])`."""
        if self._rebuild:
            self._fen_build()

        _fen_tree = self._fen_tree
        x = 0
        while end:
            x += _fen_tree[end - 1]
            end &= end - 1
        return x

    def _fen_findkth(self, k):
        """Return a pair of (the largest `idx` such that `sum(_fen_tree[:idx]) <= k`, `k - sum(_fen_tree[:idx])`)."""
        _list_lens = self._list_lens
        if k < _list_lens[0]:
            return 0, k
        if k >= self._len - _list_lens[-1]:
            return len(_list_lens) - 1, k + _list_lens[-1] - self._len
        if self._rebuild:
            self._fen_build()

        _fen_tree = self._fen_tree
        idx = -1
        for d in reversed(range(len(_fen_tree).bit_length())):
            right_idx = idx + (1 << d)
            if right_idx < len(_fen_tree) and k >= _fen_tree[right_idx]:
                idx = right_idx
                k -= _fen_tree[idx]
        return idx + 1, k

    def _delete(self, pos, idx):
        """Delete value at the given `(pos, idx)`."""
        _lists = self._lists
        _mins = self._mins
        _list_lens = self._list_lens

        self._len -= 1
        self._fen_update(pos, -1)
        del _lists[pos][idx]
        _list_lens[pos] -= 1

        if _list_lens[pos]:
            _mins[pos] = _lists[pos][0]
        else:
            del _lists[pos]
            del _list_lens[pos]
            del _mins[pos]
            self._rebuild = True

    def _loc_left(self, value):
        """Return an index pair that corresponds to the first position of `value` in the sorted list."""
        if not self._len:
            return 0, 0

        _lists = self._lists
        _mins = self._mins

        lo, pos = -1, len(_lists) - 1
        while lo + 1 < pos:
            mi = (lo + pos) >> 1
            if value <= _mins[mi]:
                pos = mi
            else:
                lo = mi

        if pos and value <= _lists[pos - 1][-1]:
            pos -= 1

        _list = _lists[pos]
        lo, idx = -1, len(_list)
        while lo + 1 < idx:
            mi = (lo + idx) >> 1
            if value <= _list[mi]:
                idx = mi
            else:
                lo = mi

        return pos, idx

    def _loc_right(self, value):
        """Return an index pair that corresponds to the last position of `value` in the sorted list."""
        if not self._len:
            return 0, 0

        _lists = self._lists
        _mins = self._mins

        pos, hi = 0, len(_lists)
        while pos + 1 < hi:
            mi = (pos + hi) >> 1
            if value < _mins[mi]:
                hi = mi
            else:
                pos = mi

        _list = _lists[pos]
        lo, idx = -1, len(_list)
        while lo + 1 < idx:
            mi = (lo + idx) >> 1
            if value < _list[mi]:
                idx = mi
            else:
                lo = mi

        return pos, idx

    def add(self, value):
        """Add `value` to sorted list."""
        _load = self._load
        _lists = self._lists
        _mins = self._mins
        _list_lens = self._list_lens

        self._len += 1
        if _lists:
            pos, idx = self._loc_right(value)
            self._fen_update(pos, 1)
            _list = _lists[pos]
            _list.insert(idx, value)
            _list_lens[pos] += 1
            _mins[pos] = _list[0]
            if _load + _load < len(_list):
                _lists.insert(pos + 1, _list[_load:])
                _list_lens.insert(pos + 1, len(_list) - _load)
                _mins.insert(pos + 1, _list[_load])
                _list_lens[pos] = _load
                del _list[_load:]
                self._rebuild = True
        else:
            _lists.append([value])
            _mins.append(value)
            _list_lens.append(1)
            self._rebuild = True

    def discard(self, value):
        """Remove `value` from sorted list if it is a member."""
        _lists = self._lists
        if _lists:
            pos, idx = self._loc_right(value)
            if idx and _lists[pos][idx - 1] == value:
                self._delete(pos, idx - 1)

    def remove(self, value):
        """Remove `value` from sorted list; `value` must be a member."""
        _len = self._len
        self.discard(value)
        if _len == self._len:
            raise ValueError('{0!r} not in list'.format(value))

    def pop(self, index=-1):
        """Remove and return value at `index` in sorted list."""
        pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
        value = self._lists[pos][idx]
        self._delete(pos, idx)
        return value

    def bisect_left(self, value):
        """Return the first index to insert `value` in the sorted list."""
        pos, idx = self._loc_left(value)
        return self._fen_query(pos) + idx

    def bisect_right(self, value):
        """Return the last index to insert `value` in the sorted list."""
        pos, idx = self._loc_right(value)
        return self._fen_query(pos) + idx

    def count(self, value):
        """Return number of occurrences of `value` in the sorted list."""
        return self.bisect_right(value) - self.bisect_left(value)

    def __len__(self):
        """Return the size of the sorted list."""
        return self._len

    def __getitem__(self, index):
        """Lookup value at `index` in sorted list."""
        pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
        return self._lists[pos][idx]

    def __delitem__(self, index):
        """Remove value at `index` from sorted list."""
        pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
        self._delete(pos, idx)

    def __contains__(self, value):
        """Return true if `value` is an element of the sorted list."""
        _lists = self._lists
        if _lists:
            pos, idx = self._loc_left(value)
            return idx < len(_lists[pos]) and _lists[pos][idx] == value
        return False

    def __iter__(self):
        """Return an iterator over the sorted list."""
        return (value for _list in self._lists for value in _list)

    def __reversed__(self):
        """Return a reverse iterator over the sorted list."""
        return (value for _list in reversed(self._lists) for value in reversed(_list))

    def __repr__(self):
        """Return string representation of sorted list."""
        return 'SortedList({0})'.format(list(self))

n,m=mdata()
hor=[mdata() for i in range(n)]
ver=[mdata() for i in range(m)]
topVer=SortedList()
botVer=SortedList()
ans=1
for x,bot,top in ver:
    if bot==0:
        botVer.add(x)
        if top==10**6:
            ans+=1
    else:
        topVer.add(x)
hor.sort(key=lambda x:x[0],reverse=True)
ver.sort(key=lambda x:x[1],reverse=True)
ind1,i=0,0
while i<n:
    if hor[i][1]==0 and hor[i][2]==10**6:
        ans+=1
    while ind1<m and topVer and ver[ind1][1]>hor[i][0]:
        topVer.remove(ver[ind1][0])
        ind1+=1
    if hor[i][1]==0:
        ans+=topVer.bisect_right(hor[i][2])
    else:
        ans+=len(topVer)-topVer.bisect_left(hor[i][1])
    i+=1

hor.reverse()
ver.sort(key=lambda x:x[2])
ind1,i=0,0
while i<n and botVer:
    while ind1<m and botVer and ver[ind1][2]<hor[i][0]:
        botVer.remove(ver[ind1][0])
        ind1+=1
    if hor[i][1]==0:
        ans+=botVer.bisect_right(hor[i][2])
    else:
        ans+=len(botVer)-botVer.bisect_left(hor[i][1])
    i+=1
out(ans)
```