class Solution {
    private Boolean[][] memo;

    public boolean isInterleave(String s1, String s2, String s3) {
        if (s3.length() != s1.length() + s2.length()) {
            return false;
        }
        memo = new Boolean[s1.length() + 1][s2.length() + 1];
        return helper(s1, s2, s3, 0, 0);
    }

    private boolean helper(String s1, String s2, String s3, int pos1, int pos2) {
        if (memo[pos1][pos2] != null) {
            return memo[pos1][pos2];
        }
        if (pos1 == s1.length()) {
            return memo[pos1][pos2] = s2.substring(pos2).equals(s3.substring(s3.length() - s2.length() + pos2));
        }
        if (pos2 == s2.length()) {
            return memo[pos1][pos2] = s1.substring(pos1).equals(s3.substring(s3.length() - s1.length() + pos1));
        }
        if (s1.charAt(pos1) == s3.charAt(pos1 + pos2)) {
            if (helper(s1, s2, s3, pos1 + 1, pos2)) {
                return memo[pos1][pos2] = true;
            }
        }
        if (s2.charAt(pos2) == s3.charAt(pos1 + pos2)) {
            if (helper(s1, s2, s3, pos1, pos2 + 1)) {
                return memo[pos1][pos2] = true;
            }
        }
        return memo[pos1][pos2] = false;
    }

}

class Solution {
    public int[] sortArray(int[] nums) {
        mergeSort(nums, nums.clone(), 0, nums.length - 1);
        return nums;
    }

    private void swap(int[] nums, int i, int j) {
        int temp = nums[i];
        nums[i] = nums[j];
        nums[j] = temp;
    }

    // Bubble Sort 最大值到最后一个位置, 次大到倒数第二个...
    public void bubbleSort(int[] nums) {
        int inPlaceCount = 0;
        // We have nums.length numbers to process in order to let each of them be in
        // the right place
        for (int i = 0; i < nums.length - 1; i++) {
            boolean isSorted = true;
            // We don't bother the nums that are in place which is the last
            // "inPlaceCount" nums.
            for (int j = 0; j < nums.length - inPlaceCount - 1; j++) {
                if (nums[j] > nums[j + 1]) {
                    isSorted = false;
                    swap(nums, j, j + 1);
                }
            }
            // End the outer for loop earlier.
            if (isSorted)
                break;
            inPlaceCount += 1;
        }
        return nums;
    }

    // Selection Sort 第0个位置最小的坐,第1个位置次小的坐...
    public void selectionSort(int[] nums) {
        for (int i = 0; i < nums.length - 1; i++) {
            int minIdx = i;
            for (int j = i; j < nums.length; j++) {
                if (nums[j] < nums[minIdx]) {
                    minIdx = j;
                }
            }
            swap(nums, minIdx, i);
        }
        return nums;
    }

    // Insertion Sort 当前位置的值比前一个小,那就换到前面,一直到换不动为止
    public void insertionSort(int[] nums) {
        for (int i = 1; i < nums.length; i++) {
            for (int j = i; j > 0; j--) {
                if (nums[j] < nums[j - 1]) {
                    swap(nums, j, j - 1);
                } else {
                    break;
                }
            }
        }
        return nums;
    }

    // Quick Sort
    private void quickSort(int[] nums, int start, int end) {
        if (start >= end) {
            return;
        }
        int pivot = start, left = start + 1, right = end;
        while (left <= right) {
            if (nums[left] > nums[pivot] && nums[right] < nums[pivot]) {
                swap(nums, left, right);
                left += 1;
                right -= 1;
                continue;
            }
            if (nums[left] <= nums[pivot]) {
                left += 1;
            }
            if (nums[right] >= nums[pivot]) {
                right -= 1;
            }
        }
        swap(nums, pivot, right);
        boolean isLeftShorter = right - start <= end - right ? true : false;
        if (isLeftShorter) {
            quickSort(nums, start, right - 1);
            quickSort(nums, right + 1, end);
        } else {
            quickSort(nums, right + 1, end);
            quickSort(nums, start, right - 1);
        }
    }

    // Merge Sort 给一个范围, 能把这个范围内的数字给sort好. 注意nums和aux往下传递的时候要颠倒位置.
    private void mergeSort(int[] nums, int[] aux, int start, int end) {
        if (start >= end) {
            return;
        }
        int mid = start + (end - start) / 2;
        mergeSort(aux, nums, start, mid);
        mergeSort(aux, nums, mid + 1, end);
        merge(nums, aux, start, mid, end);
    }

    private void merge(int[] nums, int[] aux, int left, int middle, int right) {
        int ptr = left, ptrOne = left, ptrTwo = middle + 1;
        while (ptrOne <= middle && ptrTwo <= right) {
            if (aux[ptrOne] <= aux[ptrTwo]) {
                nums[ptr++] = aux[ptrOne++];
            } else {
                nums[ptr++] = aux[ptrTwo++];
            }
        }
        while (ptrOne <= middle) {
            nums[ptr++] = aux[ptrOne++];
        }
        while (ptrTwo <= right) {
            nums[ptr++] = aux[ptrTwo++];
        }
    }
}

class Solution {
    private Map<Integer, List<Integer>> numIdxMap;
    private Random rand;

    public Solution(int[] nums) {
        numIdxMap = new HashMap<>();
        rand = new Random();
        for (int i = 0; i < nums.length; i++) {
            numIdxMap.putIfAbsent(nums[i], new ArrayList<>());
            numIdxMap.get(nums[i]).add(i);
        }
    }

    public int pick(int target) {
        List<Integer> targetIdxList = numIdxMap.get(target);
        return targetIdxList.get(rand.nextInt(targetIdxList.size()));
    }
}

System.out.println("Hello, World!");

class NumArray {
    private int[] prefixArray;

    public NumArray(int[] nums) {
        int sum = 0;
        prefixArray = new int[nums.length];
        for (int i = 0; i < nums.length; i++) {
            sum += nums[i];
            prefixArray[i] = sum;
        }
    }

    public int sumRange(int left, int right) {
        return left == 0 ? prefixArray[right] : prefixArray[right] - prefixArray[left - 1];
    }
}

class Solution {
    public int minimumTotal(List<List<Integer>> triangle) {
        if (triangle.size() == 0 || triangle.get(0).size() == 0) {
            return 0;
        }
        Deque<Pair<Integer, Integer>> indexQ = new ArrayDeque<>();
        indexQ.offer(new Pair(0, triangle.get(0).get(0)));
        int level = 0;
        for (level = 0; level < triangle.size() - 1; level++) {
            int size = indexQ.size();
            for (int i = 0; i < size; i++) {
                Pair<Integer, Integer> currPair = indexQ.poll();
                int currIndex = currPair.getKey();
                int sumSoFar = currPair.getValue();
                if (i > 0) {
                    Pair<Integer, Integer> previousPair = indexQ.peekLast();
                    if (sumSoFar + triangle.get(level + 1).get(currIndex) < previousPair.getValue()) {
                        indexQ.pollLast();
                        indexQ.offer(new Pair(currIndex, sumSoFar + triangle.get(level + 1).get(currIndex)));
                    }
                } else {
                    indexQ.offer(new Pair(currIndex, sumSoFar + triangle.get(level + 1).get(currIndex)));
                }
                indexQ.offer(new Pair(currIndex + 1, sumSoFar + triangle.get(level + 1).get(currIndex + 1)));
            }
        }
        int min = Integer.MAX_VALUE;
        while (!indexQ.isEmpty()) {
            min = Math.min(min, indexQ.poll().getValue());
        }
        return min;
    }
}

class Solution {
    public ListNode reverseBetween(ListNode head, int left, int right) {
        if (head == null || head.next == null) {
            return head;
        }
        ListNode dummy = new ListNode(0);
        dummy.next = head;
        ListNode prev = dummy, ptr = dummy;
        for (int i = 0; i < right - left + 2; i++) {
            ptr = ptr.next;
        }
        for (int i = 0; i < left - 1; i++) {
            prev = prev.next;
            ptr = ptr.next;
        }
        ListNode start = prev.next;
        prev.next = reverse(start, right - left + 1);
        start.next = ptr;
        return dummy.next;
    }

    private ListNode reverse(ListNode node, int steps) {
        ListNode prev = null, curr = node;
        for (int i = 0; i < steps; i++) {
            ListNode next = curr.next;
            curr.next = prev;
            prev = curr;
            curr = next;
        }
        return prev;
    }
}

class Solution {
    public List<Integer> grayCode(int n) {
        List<Integer> ans = new ArrayList<>();
        Set<Integer> visited = new HashSet<>();
        ans.add(0);
        visited.add(0);
        backtrack(0, n, visited, ans);
        return ans;
    }

    private boolean backtrack(int lastElement, int n, Set<Integer> visited, List<Integer> ans) {
        if (ans.size() == Math.pow(2, n)) {
            return true;
        }
        for (int i = 0; i < n; i++) {
            int currElement = ans.size() == Math.pow(2, n) - 1 ? ans.get(0) ^ (1 << i) : lastElement ^ (1 << i);
            if (!visited.contains(currElement)) {
                visited.add(currElement);
                ans.add(currElement);
                if (backtrack(currElement, n, visited, ans)) {
                    return true;
                }
                visited.remove(currElement);
                ans.remove(ans.size() - 1);
            }
        }
        return false;
    }
}

class Solution {
    public ListNode partition(ListNode head, int x) {
        if (head == null || head.next == null) {
            return head;
        }
        ListNode list1 = new ListNode(0);
        ListNode list2 = new ListNode(0);
        ListNode ptr1 = list1, ptr2 = list2, ptr3 = head;
        while (ptr3 != null) {
            if (ptr3.val < x) {
                ptr1.next = ptr3;
                ptr1 = ptr1.next;
            } else {
                ptr2.next = ptr3;
                ptr2 = ptr2.next;
            }
            ptr3 = ptr3.next;
        }
        ptr1.next = list2.next;
        ptr2.next = null;
        return list1.next;
    }
}

class Solution {
    public ListNode deleteDuplicates(ListNode head) {
        if (head == null || head.next == null) {
            return head;
        }
        ListNode dummy = new ListNode(0);
        ListNode curr = head, ptr = head, prev = dummy;
        dummy.next = head;
        while (curr != null) {
            int count = 0;
            while (ptr != null && ptr.val == curr.val) {
                ptr = ptr.next;
                count += 1;
            }
            if (count > 1) {
                prev.next = ptr;
            } else {
                prev = curr;
            }
            curr = ptr;
        }
        return dummy.next;
    }
}