Looking at Towers (difficult version)

#include <bits/stdc++.h>
using namespace std;

using ll = long long;

void setIO() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
}

const int MOD = 998244353;

int addmod(int a, int b) {
    a += b;
    if (a >= MOD) a -= MOD;
    return a;
}

int mulmod(int a, int b) {
    return int(1LL * a * b % MOD);
}

struct SegTree {
    int n;
    vector<int> val, lazy;

    SegTree(int n = 0) { init(n); }

    void init(int n_) {
        n = n_;
        val.assign(n, 0);
        lazy.assign(4 * max(1, n), 1);
    }

    void apply(int v, int x) {
        lazy[v] = mulmod(lazy[v], x);
    }

    void push(int v) {
        if (lazy[v] == 1) return;
        apply(v * 2, lazy[v]);
        apply(v * 2 + 1, lazy[v]);
        lazy[v] = 1;
    }

    void rangeMul(int v, int l, int r, int ql, int qr, int x) {
        if (ql >= qr) return;
        if (ql == l && qr == r) {
            apply(v, x);
            return;
        }
        push(v);
        int mid = (l + r) / 2;
        rangeMul(v * 2, l, mid, ql, min(qr, mid), x);
        rangeMul(v * 2 + 1, mid, r, max(ql, mid), qr, x);
    }

    void rangeMul(int l, int r, int x) {
        rangeMul(1, 0, n, l, r, x);
    }

    int get(int v, int l, int r, int pos) {
        if (r - l == 1) return mulmod(val[l], lazy[v]);
        push(v);
        int mid = (l + r) / 2;
        if (pos < mid) return get(v * 2, l, mid, pos);
        return get(v * 2 + 1, mid, r, pos);
    }

    int get(int pos) {
        return get(1, 0, n, pos);
    }

    void pointAdd(int v, int l, int r, int pos, int x) {
        if (r - l == 1) {
            val[l] = addmod(mulmod(val[l], lazy[v]), x);
            lazy[v] = 1;
            return;
        }
        push(v);
        int mid = (l + r) / 2;
        if (pos < mid) pointAdd(v * 2, l, mid, pos, x);
        else pointAdd(v * 2 + 1, mid, r, pos, x);
    }

    void pointAdd(int pos, int x) {
        pointAdd(1, 0, n, pos, x);
    }
};

vector<ll> visibleFromLeft(const vector<ll>& a) {
    vector<ll> res;
    ll cur = -1;
    for (ll x : a) {
        if (x > cur) {
            res.push_back(x);
            cur = x;
        }
    }
    return res;
}

vector<int> calc(const vector<ll>& a, const vector<ll>& b) {
    int n = int(a.size());
    int m = int(b.size());
    vector<int> res(n, 0);
    SegTree st(m + 1);
    st.pointAdd(0, 1);

    ll mx = b.back();
    for (int i = 0; i < n; i++) {
        ll x = a[i];
        if (x > mx) continue;

        if (x == mx) res[i] = st.get(m - 1);

        int lf = int(lower_bound(b.begin(), b.end(), x) - b.begin());
        st.rangeMul(lf + 1, m + 1, 2);

        if (lf < m && b[lf] == x) {
            int cur = st.get(lf);
            st.pointAdd(lf + 1, cur);
        }
    }
    return res;
}

void solve() {
    int n;
    cin >> n;
    vector<ll> a(n);
    for (ll &x : a) cin >> x;

    vector<ll> leftView = visibleFromLeft(a);

    vector<ll> rev = a;
    reverse(rev.begin(), rev.end());
    vector<ll> rightView = visibleFromLeft(rev);

    vector<int> dpL = calc(a, leftView);
    vector<int> dpR = calc(rev, rightView);
    reverse(dpR.begin(), dpR.end());

    ll mx = *max_element(a.begin(), a.end());
    int ans = 0;
    int sumLeft = 0;

    for (int i = 0; i < n; i++) {
        if (a[i] == mx) {
            ans = addmod(ans, mulmod(addmod(sumLeft, dpL[i]), dpR[i]));
        }
        sumLeft = mulmod(sumLeft, 2);
        if (a[i] == mx) {
            sumLeft = addmod(sumLeft, dpL[i]);
        }
    }

    cout << ans << '\n';
}

int main() {
    setIO();

    int t;
    cin >> t;
    while (t--) solve();
}