#include <bits/stdc++.h>
using namespace std;
using ll = long long;
constexpr int mod = 998244353;
ll _inv(ll a, ll m = mod) {
  ll b = m, u = 1, v = 0;
  while (b) {
    ll t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= m;
  if (u < 0) u += m;
  return u;
}
int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  vector<vector<ll>> dp(n + 1, vector<ll>(2, 0));
  vector<ll> sum(2);
  vector<stack<pair<int, ll>>> st(2);
  dp[0][0] = 1;
  for (int i = 0; i < n; i++) {
    vector<ll> tmp(2);
    for (int j = 0; j < 2; j++) {
      while (!st[j].empty() && st[j].top().first > a[i]) {
        (sum[j] += mod - st[j].top().second) %= mod;
        (tmp[j] += st[j].top().second * a[i] % mod * _inv(st[j].top().first) %
                   mod) %= mod;
        st[j].pop();
      }
      dp[i + 1][1 - j] = (tmp[j] + sum[j] + dp[i][1 - j] * a[i]) % mod;
      st[j].push({a[i], (tmp[j] + dp[i][1 - j] * a[i]) % mod});
      (sum[j] += st[j].top().second) %= mod;
    }
    swap(st[0], st[1]), swap(sum[0], sum[1]);
  }
  cout << (dp[n][0] - dp[n][1] + mod) % mod << endl;
}

### Prompt

Develop a solution in cpp to the problem described below:

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;
using ll = long long;
constexpr int mod = 998244353;
ll _inv(ll a, ll m = mod) {
  ll b = m, u = 1, v = 0;
  while (b) {
    ll t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= m;
  if (u < 0) u += m;
  return u;
}
int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  vector<vector<ll>> dp(n + 1, vector<ll>(2, 0));
  vector<ll> sum(2);
  vector<stack<pair<int, ll>>> st(2);
  dp[0][0] = 1;
  for (int i = 0; i < n; i++) {
    vector<ll> tmp(2);
    for (int j = 0; j < 2; j++) {
      while (!st[j].empty() && st[j].top().first > a[i]) {
        (sum[j] += mod - st[j].top().second) %= mod;
        (tmp[j] += st[j].top().second * a[i] % mod * _inv(st[j].top().first) %
                   mod) %= mod;
        st[j].pop();
      }
      dp[i + 1][1 - j] = (tmp[j] + sum[j] + dp[i][1 - j] * a[i]) % mod;
      st[j].push({a[i], (tmp[j] + dp[i][1 - j] * a[i]) % mod});
      (sum[j] += st[j].top().second) %= mod;
    }
    swap(st[0], st[1]), swap(sum[0], sum[1]);
  }
  cout << (dp[n][0] - dp[n][1] + mod) % mod << endl;
}

```