#include <bits/stdc++.h>
using namespace std;
inline long long read() {
  long long x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') f = ch == '-' ? -1 : 1, ch = getchar();
  while (ch >= '0' && ch <= '9') x = x * 10 + ch - 48, ch = getchar();
  return x * f;
}
const long long N(2e5 + 10);
const long long mod(998244353);
long long n;
long long a[N];
long long g[N];
long long s[N];
long long pre[N];
long long nxt[N];
long long stk[N];
signed main() {
  n = read();
  a[1] = a[n + 2] = -1e9;
  long long top = 1;
  stk[1] = 1;
  for (long long i = (2); i <= (n + 1); i++) a[i] = read();
  for (long long i = (2); i <= (n + 2); i++) {
    for (; top && a[stk[top]] >= a[i]; top--) nxt[stk[top]] = i;
    pre[i] = stk[top], stk[++top] = i;
  }
  s[1] = 1;
  for (long long i = (2); i <= (n + 1); i++) {
    long long x = s[i - 1] - s[pre[i] - 1] + mod;
    x = (x % mod * a[i]) % mod, (g[i] += g[i - 1] + x) %= mod;
    (g[nxt[i]] += mod - x) %= mod, s[i] = (s[i - 1] + mod - g[i]) % mod;
  }
  if ((n + 1) & 1) g[n + 1] = mod - g[n + 1];
  cout << g[n + 1] % mod;
  return 0;
}

### Prompt

Please formulate a cpp solution to 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;
inline long long read() {
  long long x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') f = ch == '-' ? -1 : 1, ch = getchar();
  while (ch >= '0' && ch <= '9') x = x * 10 + ch - 48, ch = getchar();
  return x * f;
}
const long long N(2e5 + 10);
const long long mod(998244353);
long long n;
long long a[N];
long long g[N];
long long s[N];
long long pre[N];
long long nxt[N];
long long stk[N];
signed main() {
  n = read();
  a[1] = a[n + 2] = -1e9;
  long long top = 1;
  stk[1] = 1;
  for (long long i = (2); i <= (n + 1); i++) a[i] = read();
  for (long long i = (2); i <= (n + 2); i++) {
    for (; top && a[stk[top]] >= a[i]; top--) nxt[stk[top]] = i;
    pre[i] = stk[top], stk[++top] = i;
  }
  s[1] = 1;
  for (long long i = (2); i <= (n + 1); i++) {
    long long x = s[i - 1] - s[pre[i] - 1] + mod;
    x = (x % mod * a[i]) % mod, (g[i] += g[i - 1] + x) %= mod;
    (g[nxt[i]] += mod - x) %= mod, s[i] = (s[i - 1] + mod - g[i]) % mod;
  }
  if ((n + 1) & 1) g[n + 1] = mod - g[n + 1];
  cout << g[n + 1] % mod;
  return 0;
}

```