description: You are given an array of n positive integers a_1, a_2, …, a_n. Your task is to calculate the number of arrays of n positive integers b_1, b_2, …, b_n such that: 
  
    * 1 ≤ b_i ≤ a_i for every i (1 ≤ i ≤ n), and 
    * b_i ≠ b_{i+1} for every i (1 ≤ i ≤ n - 1). 
  
  
  
  The number of such arrays can be very large, so print it modulo 998 244 353.
  
  Input
  
  The first line contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the array a.
  
  The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9).
  
  Output
  
  Print the answer modulo 998 244 353 in a single line.
  
  Examples
  
  Input
  
  
  3
  2 2 2
  
  
  Output
  
  
  2
  
  Input
  
  
  2
  2 3
  
  
  Output
  
  
  4
  
  Input
  
  
  3
  1 1 1
  
  
  Output
  
  
  0
  
  Note
  
  In the first test case possible arrays are [1, 2, 1] and [2, 1, 2].
  
  In the second test case possible arrays are [1, 2], [1, 3], [2, 1] and [2, 3].
solution: #include <bits/stdc++.h>
  using namespace std;
  const long long P = 998244353;
  inline long long mod(long long x) {
    long long y = x % P;
    return y < 0 ? y + P : y;
  }
  struct Node {
    struct Node *left = nullptr, *right = nullptr;
    long long sum = 0, lazy = 0;
    bool toShift = false;
  };
  void push(Node *node, long long l, long long m, long long r) {
    if (not node->left) node->left = new Node();
    if (not node->right) node->right = new Node();
    if (not node->toShift) return;
    node->left->sum = mod((m - l) * node->lazy);
    node->left->lazy = node->lazy;
    node->left->toShift = true;
    node->right->sum = mod((r - m) * node->lazy);
    node->right->lazy = node->lazy;
    node->right->toShift = true;
    node->toShift = false;
  }
  void update(Node *node, long long l, long long r, long long l1, long long r1,
              long long v) {
    if (l1 == r1) return;
    if (l == l1 and r == r1) {
      node->sum = mod((r - l) * v);
      node->lazy = v;
      node->toShift = true;
      return;
    }
    long long m = (l + r) >> 1;
    push(node, l, m, r);
    update(node->left, l, m, min(l1, m), min(r1, m), v);
    update(node->right, m, r, max(l1, m), max(r1, m), v);
    node->sum = mod(node->left->sum + node->right->sum);
  }
  void test() {
    long long n;
    cin >> n;
    vector<long long> a(n);
    for (long long &a1 : a) cin >> a1;
    Node *seg = new Node();
    long long l = 1, r = 1e9 + 1;
    long long m = 1, k = 0;
    update(seg, l, r, 1, a[0] + 1, 1);
    for (long long i = 1; i < n; i++) {
      long long s = mod(m * seg->sum + k * (r - l));
      m = -m;
      k = mod(s - k);
      long long v = mod(-k / m);
      update(seg, l, r, a[i] + 1, r, v);
    }
    cout << mod(m * seg->sum + k * (r - l)) << '\n';
  }
  signed main() {
    iostream::sync_with_stdio(false);
    long long q = 1;
    while (q--) test();
    assert(cin);
  }
  