Problem:
Score : 400 points

Problem Statement

There are N islands lining up from west to east, connected by N-1 bridges.

The i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.

One day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:

Request i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.

You decided to remove some bridges to meet all these M requests.

Find the minimum number of bridges that must be removed.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq a_i < b_i \leq N

All pairs (a_i, b_i) are distinct.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print the minimum number of bridges that must be removed.

Sample Input 1

5 2
1 4
2 5

Sample Output 1

1

The requests can be met by removing the bridge connecting the second and third islands from the west.

Sample Input 2

9 5
1 8
2 7
3 5
4 6
7 9

Sample Output 2

2

Sample Input 3

5 10
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5

Sample Output 3

4

Solution in Python (3.4.3) (judge verdict: Time Limit Exceeded)

headData = [int(n) for n in input().split()]
islandNum = headData[0]
requestNum = headData[1]
requestList = []
count = 0
for n in range(requestNum):
    request = [int(elem) for elem in input().split()]
    requestList.append(request)


while (len(requestList) != 0):
    # 優先度チェック
    bridgePriority = islandNum * [0]
    for request in requestList:
        for j in range(request[0], request[1]):
            bridgePriority[j] += 1
    bridge = -1

    # 優先度が最も高い橋を特定
    for index in range(len(bridgePriority)):
        if (bridgePriority[index] == max(bridgePriority)):
            bridge = index
            break

    # 橋を削除した場合、叶っていないリクエストリストを作成
    newRequestList = []
    for request in requestList:
        if (bridge < request[0] or request[1] <= bridge):
            newRequestList.append(request)
    requestList = newRequestList
    count += 1

print(count)