#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 8, inf = 1e9 + 7, mod = 998244353;
const long long mod2 = (long long)mod * mod;
int n;
int a[N];
struct Node {
  Node *l, *r;
  int len;
  bool reset_, laz;
  long long la2, val;
  Node(int len)
      : l(NULL), r(NULL), len(len), reset_(false), laz(false), la2(0), val(0) {}
  void reset() {
    reset_ = true;
    laz = la2 = val = 0;
  }
  void upd() {
    laz ^= 1;
    la2 = mod - la2;
    val = mod - val;
  }
  void upd(long long v) {
    la2 += v;
    if (la2 >= mod) la2 -= mod;
    (val += v * len) %= mod;
  }
  void down() {
    if (reset_) {
      l->reset();
      r->reset();
      reset_ = false;
    }
    if (laz) {
      l->upd();
      r->upd();
      laz = false;
    }
    if (la2) {
      l->upd(la2);
      r->upd(la2);
      la2 = 0;
    }
  }
} * root(new Node(inf));
void upd(Node *u, int l, int r, int a, int b, long long v) {
  if (b < l || r < a) return;
  if (a <= l && r <= b) {
    if (v == -2)
      u->reset();
    else {
      if (~v)
        u->upd(v);
      else
        u->upd();
    }
    return;
  }
  int m = (l + r) >> 1;
  if (!u->l) u->l = new Node(m - l + 1);
  if (!u->r) u->r = new Node(r - l);
  u->down();
  upd(u->l, l, m, a, b, v);
  upd(u->r, m + 1, r, a, b, v);
  u->val = (u->l->val + u->r->val) % mod;
}
long long get(Node *u, int l, int r, int a, int b) {
  if (b < l || r < a) return 0;
  if (a <= l && r <= b) return u->val;
  int m = (l + r) >> 1;
  if (!u->l) u->l = new Node(m - l + 1);
  if (!u->r) u->r = new Node(r - l);
  u->down();
  return get(u->l, l, m, a, b) + get(u->r, m + 1, r, a, b);
}
long long sum[N];
int main() {
  cin.tie(NULL)->sync_with_stdio(false);
  cin >> n;
  for (int i = 1; i <= n; ++i) cin >> a[i];
  sum[0] = 1;
  for (int i = 1; i <= n; ++i) {
    sum[i] =
        (a[i] * sum[i - 1] - get(root, 1, inf, 1, min(a[i - 1], a[i])) + mod2) %
        mod;
    upd(root, 1, inf, a[i - 1] + 1, inf, -2);
    upd(root, 1, inf, 1, a[i - 1], -1);
    upd(root, 1, inf, 1, a[i], sum[i - 1]);
  }
  cout << sum[n] << '\n';
}

### Prompt

In Cpp, your task is to solve the following problem:

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].

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 8, inf = 1e9 + 7, mod = 998244353;
const long long mod2 = (long long)mod * mod;
int n;
int a[N];
struct Node {
  Node *l, *r;
  int len;
  bool reset_, laz;
  long long la2, val;
  Node(int len)
      : l(NULL), r(NULL), len(len), reset_(false), laz(false), la2(0), val(0) {}
  void reset() {
    reset_ = true;
    laz = la2 = val = 0;
  }
  void upd() {
    laz ^= 1;
    la2 = mod - la2;
    val = mod - val;
  }
  void upd(long long v) {
    la2 += v;
    if (la2 >= mod) la2 -= mod;
    (val += v * len) %= mod;
  }
  void down() {
    if (reset_) {
      l->reset();
      r->reset();
      reset_ = false;
    }
    if (laz) {
      l->upd();
      r->upd();
      laz = false;
    }
    if (la2) {
      l->upd(la2);
      r->upd(la2);
      la2 = 0;
    }
  }
} * root(new Node(inf));
void upd(Node *u, int l, int r, int a, int b, long long v) {
  if (b < l || r < a) return;
  if (a <= l && r <= b) {
    if (v == -2)
      u->reset();
    else {
      if (~v)
        u->upd(v);
      else
        u->upd();
    }
    return;
  }
  int m = (l + r) >> 1;
  if (!u->l) u->l = new Node(m - l + 1);
  if (!u->r) u->r = new Node(r - l);
  u->down();
  upd(u->l, l, m, a, b, v);
  upd(u->r, m + 1, r, a, b, v);
  u->val = (u->l->val + u->r->val) % mod;
}
long long get(Node *u, int l, int r, int a, int b) {
  if (b < l || r < a) return 0;
  if (a <= l && r <= b) return u->val;
  int m = (l + r) >> 1;
  if (!u->l) u->l = new Node(m - l + 1);
  if (!u->r) u->r = new Node(r - l);
  u->down();
  return get(u->l, l, m, a, b) + get(u->r, m + 1, r, a, b);
}
long long sum[N];
int main() {
  cin.tie(NULL)->sync_with_stdio(false);
  cin >> n;
  for (int i = 1; i <= n; ++i) cin >> a[i];
  sum[0] = 1;
  for (int i = 1; i <= n; ++i) {
    sum[i] =
        (a[i] * sum[i - 1] - get(root, 1, inf, 1, min(a[i - 1], a[i])) + mod2) %
        mod;
    upd(root, 1, inf, a[i - 1] + 1, inf, -2);
    upd(root, 1, inf, 1, a[i - 1], -1);
    upd(root, 1, inf, 1, a[i], sum[i - 1]);
  }
  cout << sum[n] << '\n';
}

```