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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for (int (i)=(0);(i)<(long long)(n);++(i))
using ll = long long;
using P = pair<int, int>;
using namespace std;

template<class T> void vin(vector<T>& v, int n) {
    v.resize(n);
    for (int i = 0; i < n; ++i) {
        cin >> v[i];
    }
}

struct SegmentTree {
    int n;
    vector<int> node;
    SegmentTree(vector<int> v) {
        n = 1;
        while (n < v.size()) n *= 2;
        node.resize(2*n-1, INT_MAX);
        for (int i=0; i<v.size(); ++i) node[i+n-1] = v[i];
        for (int i=n-2; i>=0; --i) node[i] = min(node[i * 2 + 1], node[i * 2 + 2]);
    }
    SegmentTree(int N) {
        n = 1;
        while (n < N) n *= 2;
        node.resize(2*n-1, INT_MAX);
    }
    // x番目の要素をvalに更新
    void update(int x, int val) {
        x += (n - 1);
        node[x] = val;
        while (x > 0) {
            x = (x - 1) / 2;
            node[x] = min(node[2 * x + 1], node[2 * x + 2]);
        }
    }
    // [a, b)の中の要素の最小値を答える
    // k := 自分がいるノードのインデックス
    int query(int a, int b, int k=0, int l=0, int r=-1) {
        if (r < 0) r = n;
        if (r <= a || b <= l) return INT_MAX;
        if (a <= l and r <= b) return node[k];
        int vl = query(a, b, 2*k+1, l, (l+r)/2);
        int vr = query(a, b, 2*k+2, (l+r)/2, r);
        return min(vl, vr);
    }
};

int arr1[101010];
int arr2[101010];

int main() {
    int n, m;
    cin >> n >> m;
    SegmentTree seg(n);
    rep(i, m) {
        int a, b;
        cin >> a >> b;
        a--;
        b--;
        arr1[a]++;
        arr2[b]++;
    }
    int ans=0;
    bool flag=false;
    rep(i, n) {
        if (arr2[i] > 0 and flag) {
            flag = false;
            ans++;
        }
        if (arr1[i] > 0) {
            flag = true;
        }
    }
    cout << ans << endl;
}