#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1e5 + 5;
const int MOD = 998244353;
int t, n;
int a[MAXN];
vector<int> dp[2];
long long cnt[2][MAXN];
int main() {
  scanf("%d", &t);
  while (t--) {
    int pos = 0;
    long long ans = 0;
    scanf("%d", &n);
    for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
    for (int i = n; i; --i) {
      pos ^= 1;
      dp[pos].push_back(a[i]);
      cnt[pos][a[i]] = 1;
      int last = a[i];
      for (auto it : dp[pos ^ 1]) {
        int minn = (a[i] + it - 1) / it;
        int st = a[i] / minn;
        int y = cnt[pos ^ 1][it];
        cnt[pos][st] += y %= MOD;
        if ((st) != last) {
          dp[pos].push_back(st), last = st;
        }
        (ans += ((long long)i * y) * (minn - 1)) %= MOD;
      }
      for (auto x : dp[pos ^ 1]) cnt[pos ^ 1][x] = 0;
      dp[pos ^ 1].clear();
      ans %= MOD;
    }
    printf("%lld\n", ans);
    for (auto x : dp[0]) cnt[0][x] = 0;
    for (auto x : dp[1]) cnt[1][x] = 0;
    dp[0].clear();
    dp[1].clear();
  }
  return 0;
}

### Prompt

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

For an array b of n integers, the extreme value of this array is the minimum number of times (possibly, zero) the following operation has to be performed to make b non-decreasing: 

  * Select an index i such that 1 ≤ i ≤ |b|, where |b| is the current length of b. 
  * Replace b_i with two elements x and y such that x and y both are positive integers and x + y = b_i. 
  * This way, the array b changes and the next operation is performed on this modified array. 



For example, if b = [2, 4, 3] and index 2 gets selected, then the possible arrays after this operation are [2, \underline{1}, \underline{3}, 3], [2, \underline{2}, \underline{2}, 3], or [2, \underline{3}, \underline{1}, 3]. And consequently, for this array, this single operation is enough to make it non-decreasing: [2, 4, 3] → [2, \underline{2}, \underline{2}, 3].

It's easy to see that every array of positive integers can be made non-decreasing this way.

YouKn0wWho has an array a of n integers. Help him find the sum of extreme values of all nonempty subarrays of a modulo 998 244 353. If a subarray appears in a multiple times, its extreme value should be counted the number of times it appears.

An array d is a subarray of an array c if d can be obtained from c by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input

The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 10^5).

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^5).

It is guaranteed that the sum of n over all test cases doesn't exceed 10^5.

Output

For each test case, print a single integer — the sum of extreme values of all subarrays of a modulo 998 244 353.

Example

Input


4
3
5 4 3
4
3 2 1 4
1
69
8
7264 40515 28226 92776 35285 21709 75124 48163


Output


5
9
0
117

Note

Let f(l, r) denote the extreme value of [a_l, a_{l+1}, …, a_r].

In the first test case, 

  * f(1, 3) = 3, because YouKn0wWho can perform the following operations on the subarray [5, 4, 3] (the newly inserted elements are underlined):

[5, 4, 3] → [\underline{3}, \underline{2}, 4, 3] → [3, 2, \underline{2}, \underline{2}, 3] → [\underline{1}, \underline{2}, 2, 2, 2, 3];

  * f(1, 2) = 1, because [5, 4] → [\underline{2}, \underline{3}, 4];
  * f(2, 3) = 1, because [4, 3] → [\underline{1}, \underline{3}, 3];
  * f(1, 1) = f(2, 2) = f(3, 3) = 0, because they are already non-decreasing. 



So the total sum of extreme values of all subarrays of a = 3 + 1 + 1 + 0 + 0 + 0 = 5.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1e5 + 5;
const int MOD = 998244353;
int t, n;
int a[MAXN];
vector<int> dp[2];
long long cnt[2][MAXN];
int main() {
  scanf("%d", &t);
  while (t--) {
    int pos = 0;
    long long ans = 0;
    scanf("%d", &n);
    for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
    for (int i = n; i; --i) {
      pos ^= 1;
      dp[pos].push_back(a[i]);
      cnt[pos][a[i]] = 1;
      int last = a[i];
      for (auto it : dp[pos ^ 1]) {
        int minn = (a[i] + it - 1) / it;
        int st = a[i] / minn;
        int y = cnt[pos ^ 1][it];
        cnt[pos][st] += y %= MOD;
        if ((st) != last) {
          dp[pos].push_back(st), last = st;
        }
        (ans += ((long long)i * y) * (minn - 1)) %= MOD;
      }
      for (auto x : dp[pos ^ 1]) cnt[pos ^ 1][x] = 0;
      dp[pos ^ 1].clear();
      ans %= MOD;
    }
    printf("%lld\n", ans);
    for (auto x : dp[0]) cnt[0][x] = 0;
    for (auto x : dp[1]) cnt[1][x] = 0;
    dp[0].clear();
    dp[1].clear();
  }
  return 0;
}

```