<p>Given an integer array <code>nums</code>, return <em>the length of the longest <strong>strictly increasing </strong></em><span data-keyword="subsequence-array"><em><strong>subsequence</strong></em></span>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [10,9,2,5,3,7,101,18]
<strong>Output:</strong> 4
<strong>Explanation:</strong> The longest increasing subsequence is [2,3,7,101], therefore the length is 4.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [0,1,0,3,2,3]
<strong>Output:</strong> 4
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [7,7,7,7,7,7,7]
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 2500</code></li>
	<li><code>-10<sup>4</sup> &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

<p>&nbsp;</p>
<p><b>Follow up:</b>&nbsp;Can you come up with an algorithm that runs in&nbsp;<code>O(n log(n))</code> time complexity?</p>

// Segment tree Sum
    class ST {
    	int n;
    	vector<int> tree;
    public:
    	ST(const vector<int>& data) {
    		int N = data.size();
    		n = N;
    		tree.resize(2 * n);
    		for (int i = 0; i < n; i++) {
    			tree[i + n] = data[i];
    		}
    		build();
    	}
    
    	void build() {  // build the tree
    		for (int i = n - 1; i > 0; --i) tree[i] = max(tree[i<<1], tree[i<<1|1]);
    	}
    
    	void modify(int p, int value) {  // unordered_set value at position p
    		for (tree[p += n] = value; p > 1; p >>= 1) tree[p>>1] = max(tree[p], tree[p^1]);
    	}
    
    	int query(int l, int r) {  // sum on interval [l, r]
    		r++;
    		int res = 0;
    		for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
    			if (l&1) res = max(res, tree[l++]);
    			if (r&1) res = max(res, tree[--r]);
    		}
    		return res;
    	}
    };

class Solution {
public:
    int lengthOfLIS(vector<int>& a) {
        int n = a.size();

        vector<int> data(2e4 + 1, 0);
        ST st(data);

        int offset = 1e4 + 10;

        vector<int> dp(n, 0);
        dp[0] = 1;
        st.modify(a[0] + offset, dp[0]);
        // dp[i]
        for (int i = 1; i < n; i++) {
            int v = st.query(0, a[i] + offset - 1);
            dp[i] = v + 1;
            st.modify(a[i] + offset,  dp[i]);
            // int v = 0;
            // for (int j = i - 1; j >= 0; j--) {
            //     if (a[i] > a[j])
            //         v = max(v, dp[j]);
            // }
            // dp[i] = v + 1;
        }

        int ans = 0;
        for (auto e : dp) ans = max(ans, e);
        // for (auto e : dp) cout << e << " ";
        // cout << endl;

        return ans;
    }
};
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