<p>Given an integer array of even length <code>arr</code>, return <code>true</code><em> if it is possible to reorder </em><code>arr</code><em> such that </em><code>arr[2 * i + 1] = 2 * arr[2 * i]</code><em> for every </em><code>0 &lt;= i &lt; len(arr) / 2</code><em>, or </em><code>false</code><em> otherwise</em>.</p>

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

<pre>
<strong>Input:</strong> arr = [3,1,3,6]
<strong>Output:</strong> false
</pre>

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

<pre>
<strong>Input:</strong> arr = [2,1,2,6]
<strong>Output:</strong> false
</pre>

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

<pre>
<strong>Input:</strong> arr = [4,-2,2,-4]
<strong>Output:</strong> true
<strong>Explanation:</strong> We can take two groups, [-2,-4] and [2,4] to form [-2,-4,2,4] or [2,4,-2,-4].
</pre>

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

<ul>
	<li><code>2 &lt;= arr.length &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>arr.length</code> is even.</li>
	<li><code>-10<sup>5</sup> &lt;= arr[i] &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
public:
    bool canReorderDoubled(vector<int>& arr) {
        bool ret = true;
        vector<int> negarr;
        vector<bool> nused;
        vector<int> posarr;
        vector<bool> pused;

        for (int i = 0; i < arr.size(); i++) {
            if (arr[i] < 0) { 
                negarr.push_back(arr[i]);
                nused.push_back(false);
            } else {
                posarr.push_back(arr[i]);
                pused.push_back(false);
            }
        }
        if (negarr.size() > 0) {
            if (negarr.size() % 2 != 0) {
                ret = false;
            }
            if (ret) {
                sort(negarr.rbegin(), negarr.rend());

                for (int i = 0; ret && i < negarr.size(); i++) {
                    if (!nused[i]) {
                        int ele = negarr[i] * 2;
                        int beg = i + 1;
                        int end = negarr.size() - 1;
                        nused[i] = true;
                        bool f = false;
                        while(beg <= end) {
                            int mid = (beg + end)/2;
                            if (negarr[mid] == ele) {
                                for (int j = mid; j > i; j--) {
                                    if (negarr[j] == ele) {
                                        if (!nused[j]) {
                                            nused[j] = true;
                                            f = true;
                                            break;
                                        }
                                    } else {
                                        break;
                                    }
                                }
                                for (int j = mid + 1; !f && j < negarr.size(); j++) {
                                    if (negarr[j] == ele) {
                                        if (!nused[j]) {
                                            nused[j] = true;
                                            f = true;
                                            break;
                                        }
                                    } else {
                                        break;
                                    }
                                }
                                break;
                            } else if (negarr[mid] < ele) {
                                end = mid - 1;
                            } else {
                                beg = mid + 1;
                            }
                        }
                        if (!f) {
                            ret = false;
                        }
                    }
                }
            }
        }

        if (ret) {
            if (posarr.size() > 0) {
                if (posarr.size() % 2 != 0) {
                    ret = false;
                }
                if (ret) {
                    sort(posarr.begin(), posarr.end());
                    for (int i = 0; ret && i < posarr.size(); i++) {
                        if (!pused[i]) {
                            int ele = posarr[i] * 2;
                            int beg = i + 1;
                            int end = posarr.size() - 1;
                            pused[i] = true;
                            bool f = false;
                            while(beg <= end) {
                                int mid = (beg + end)/2;
                                if (posarr[mid] == ele) {
                                    for (int j = mid; j > i; j--) {
                                        if (posarr[j] == ele) {
                                            if (!pused[j]) {
                                                pused[j] = true;
                                                f = true;
                                                break;
                                            }
                                        } else {
                                            break;
                                        }
                                    }
                                    for (int j = mid + 1; !f && j < posarr.size(); j++) {
                                        if (posarr[j] == ele) {
                                            if (!pused[j]) {
                                                pused[j] = true;
                                                f = true;
                                                break;
                                            }
                                        } else {
                                            break;
                                        }
                                    }
                                    break;
                                } else if (posarr[mid] > ele) {
                                    end = mid - 1;
                                } else {
                                    beg = mid + 1;
                                }
                            }
                            if (!f) {
                                ret = false;
                            }
                        }
                    }
                }
            }
        }

        return ret;
    }
};
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