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A. The Tower is Going Home

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputOn a chessboard with a width of $$$10^9$$$ and a height of $$$10^9$$$, the rows are numbered from bottom to top from $$$1$$$ to $$$10^9$$$, and the columns are numbered from left to right from $$$1$$$ to $$$10^9$$$. Therefore, for each cell of the chessboard you can assign the coordinates $$$(x,y)$$$, where $$$x$$$ is the column number and $$$y$$$ is the row number.

Every day there are fights between black and white pieces on this board. Today, the black ones won, but at what price? Only the rook survived, and it was driven into the lower left corner — a cell with coordinates $$$(1,1)$$$. But it is still happy, because the victory has been won and it's time to celebrate it! In order to do this, the rook needs to go home, namely — on the upper side of the field (that is, in any cell that is in the row with number $$$10^9$$$).

Everything would have been fine, but the treacherous white figures put spells on some places of the field before the end of the game. There are two types of spells:

- Vertical. Each of these is defined by one number $$$x$$$. Such spells create an infinite blocking line between the columns $$$x$$$ and $$$x+1$$$.
- Horizontal. Each of these is defined by three numbers $$$x_1$$$, $$$x_2$$$, $$$y$$$. Such spells create a blocking segment that passes through the top side of the cells, which are in the row $$$y$$$ and in columns from $$$x_1$$$ to $$$x_2$$$ inclusive. The peculiarity of these spells is that it is impossible for a certain pair of such spells to have a common point. Note that horizontal spells can have common points with vertical spells.

Let's recall that the rook is a chess piece that in one move can move to any point that is in the same row or column with its initial position. In our task, the rook can move from the cell $$$(r_0,c_0)$$$ into the cell $$$(r_1,c_1)$$$ only under the condition that $$$r_1 = r_0$$$ or $$$c_1 = c_0$$$ and there is no blocking lines or blocking segments between these cells (For better understanding, look at the samples).

Fortunately, the rook can remove spells, but for this it has to put tremendous efforts, therefore, it wants to remove the minimum possible number of spells in such way, that after this it can return home. Find this number!

Input

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$0 \le n,m \le 10^5$$$) — the number of vertical and horizontal spells.

Each of the following $$$n$$$ lines contains one integer $$$x$$$ ($$$1 \le x < 10^9$$$) — the description of the vertical spell. It will create a blocking line between the columns of $$$x$$$ and $$$x+1$$$.

Each of the following $$$m$$$ lines contains three integers $$$x_1$$$, $$$x_2$$$ and $$$y$$$ ($$$1 \le x_{1} \le x_{2} \le 10^9$$$, $$$1 \le y < 10^9$$$) — the numbers that describe the horizontal spell. It will create a blocking segment that passes through the top sides of the cells that are in the row with the number $$$y$$$, in columns from $$$x_1$$$ to $$$x_2$$$ inclusive.

It is guaranteed that all spells are different, as well as the fact that for each pair of horizontal spells it is true that the segments that describe them do not have common points.

Output

In a single line print one integer — the minimum number of spells the rook needs to remove so it can get from the cell $$$(1,1)$$$ to at least one cell in the row with the number $$$10^9$$$

Examples

Input

2 3

6

8

1 5 6

1 9 4

2 4 2

Output

1

Input

1 3

4

1 5 3

1 9 4

4 6 6

Output

1

Input

0 2

1 1000000000 4

1 1000000000 2

Output

2

Input

0 0

Output

0

Input

2 3

4

6

1 4 3

1 5 2

1 6 5

Output

2

Note

In the first sample, in order for the rook return home, it is enough to remove the second horizontal spell.

In the second sample, in order for the rook to return home, it is enough to remove the only vertical spell. If we tried to remove just one of the horizontal spells, it would not allow the rook to get home, because it would be blocked from above by one of the remaining horizontal spells (either first one or second one), and to the right it would be blocked by a vertical spell.

In the third sample, we have two horizontal spells that go through the whole field. These spells can not be bypassed, so we need to remove both of them.

In the fourth sample, we have no spells, which means that we do not need to remove anything.

In the fifth example, we can remove the first vertical and third horizontal spells.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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