Ildar is the algorithm teacher of William and Harris. Today, Ildar is teaching Cartesian Tree. However, Harris is sick, so Ildar is only teaching William.

A cartesian tree is a rooted tree, that can be constructed from a sequence of distinct integers. We build the cartesian tree as follows:

  1. If the sequence is empty, return an empty tree;
  2. Let the position of the maximum element be x;
  3. Remove element on the position x from the sequence and break it into the left part and the right part (which might be empty) (not actually removing it, just taking it away temporarily);
  4. Build cartesian tree for each part;
  5. Create a new vertex for the element, that was on the position x which will serve as the root of the new tree. Then, for the root of the left part and right part, if exists, will become the children for this vertex;
  6. Return the tree we have gotten.



For example, this is the cartesian tree for the sequence 4, 2, 7, 3, 5, 6, 1:

<image>

After teaching what the cartesian tree is, Ildar has assigned homework. He starts with an empty sequence a.

In the i-th round, he inserts an element with value i somewhere in a. Then, he asks a question: what is the sum of the sizes of the subtrees for every node in the cartesian tree for the current sequence a?

Node v is in the node u subtree if and only if v = u or v is in the subtree of one of the vertex u children. The size of the subtree of node u is the number of nodes v such that v is in the subtree of u.

Ildar will do n rounds in total. The homework is the sequence of answers to the n questions.

The next day, Ildar told Harris that he has to complete the homework as well. Harris obtained the final state of the sequence a from William. However, he has no idea how to find the answers to the n questions. Help Harris!

Input

The first line contains a single integer n (1 ≤ n ≤ 150000).

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ n). It is guarenteed that each integer from 1 to n appears in the sequence exactly once.

Output

Print n lines, i-th line should contain a single integer — the answer to the i-th question.

Examples

Input


5
2 4 1 5 3


Output


1
3
6
8
11


Input


6
1 2 4 5 6 3


Output


1
3
6
8
12
17

Note

After the first round, the sequence is 1. The tree is

<image>

The answer is 1.

After the second round, the sequence is 2, 1. The tree is

<image>

The answer is 2+1=3.

After the third round, the sequence is 2, 1, 3. The tree is

<image>

The answer is 2+1+3=6.

After the fourth round, the sequence is 2, 4, 1, 3. The tree is

<image>

The answer is 1+4+1+2=8.

After the fifth round, the sequence is 2, 4, 1, 5, 3. The tree is

<image>

The answer is 1+3+1+5+1=11.
#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 10;
int a[maxn], pos[maxn];
int n;
struct segtree {
  int cnt[maxn << 2], val[maxn << 2];
  long long seg[maxn << 2];
  int tag_val[maxn << 2];
  long long get_val(int v) { return seg[v] + 1LL * cnt[v] * tag_val[v]; }
  void pushdown(int v) {
    tag_val[v << 1] += tag_val[v];
    tag_val[v << 1 | 1] += tag_val[v];
    tag_val[v] = 0;
  }
  void pushup(int v) {
    seg[v] = get_val(v << 1) + get_val(v << 1 | 1);
    cnt[v] = cnt[v << 1] + cnt[v << 1 | 1];
    val[v] = val[v << 1] + val[v << 1 | 1];
  }
  void update_val(int l, int r, int ql, int qr, int v) {
    if (ql > r || l > qr) return;
    if (ql <= l && r <= qr) {
      ++tag_val[v];
      return;
    }
    pushdown(v);
    int mid = (l + r) >> 1;
    if (ql <= mid) update_val(l, mid, ql, qr, v << 1);
    if (qr > mid) update_val(mid + 1, r, ql, qr, v << 1 | 1);
    pushup(v);
  }
  void update_cnt(int l, int r, int x, int v, int nval) {
    if (l == r) {
      cnt[v] += nval;
      return;
    }
    pushdown(v);
    int mid = (l + r) >> 1;
    if (x <= mid)
      update_cnt(l, mid, x, v << 1, nval);
    else
      update_cnt(mid + 1, r, x, v << 1 | 1, nval);
    pushup(v);
  }
  int ask_cnt(int l, int r, int x, int v) {
    if (l == r) return cnt[v];
    pushdown(v);
    int mid = (l + r) >> 1, res;
    if (x <= mid) res = ask_cnt(l, mid, x, v << 1);
    if (x > mid) res = ask_cnt(mid + 1, r, x, v << 1 | 1);
    pushup(v);
    return res;
  }
  int ask_val(int l, int r, int x, int v) {
    if (l == r) return val[v] + tag_val[v];
    pushdown(v);
    int mid = (l + r) >> 1, res;
    if (x <= mid) res = ask_cnt(l, mid, x, v << 1);
    if (x > mid) res = ask_cnt(mid + 1, r, x, v << 1 | 1);
    pushup(v);
    return res;
  }
} seg;
struct segtree_max {
  int fi[maxn << 2], se[maxn << 2], tag[maxn << 2];
  int cnt[maxn << 2];
  void pushup(int v) {
    fi[v] = min(fi[v << 1], fi[v << 1 | 1]);
    if (fi[v << 1] == fi[v << 1 | 1]) {
      cnt[v] = cnt[v << 1] + cnt[v << 1 | 1];
      se[v] = min(se[v << 1], se[v << 1 | 1]);
    } else if (fi[v << 1] < fi[v << 1 | 1]) {
      cnt[v] = cnt[v << 1];
      se[v] = min(fi[v << 1 | 1], se[v << 1]);
    } else {
      cnt[v] = cnt[v << 1 | 1];
      se[v] = min(fi[v << 1], se[v << 1 | 1]);
    }
  }
  void pushdown(int v) {
    if (tag[v]) {
      if (tag[v] > fi[v << 1]) {
        fi[v << 1] = tag[v << 1] = tag[v];
      }
      if (tag[v] > fi[v << 1 | 1]) {
        fi[v << 1 | 1] = tag[v << 1 | 1] = tag[v];
      }
      tag[v] = 0;
    }
  }
  void init(int l, int r, int v = 1) {
    if (l == r) {
      fi[v] = n + 2;
      se[v] = INT_MAX;
      cnt[v] = 1;
      return;
    }
    int mid = (l + r) >> 1;
    init(l, mid, v << 1);
    init(mid + 1, r, v << 1 | 1);
    pushup(v);
  }
  void update(int l, int r, int ql, int qr, int nval, int v) {
    if (ql > qr || ql > r || l > qr || nval <= fi[v]) return;
    if (ql <= l && r <= qr) {
      if (nval < se[v]) {
        seg.update_cnt(0, n + 1, fi[v] - 1, 1, +cnt[v]);
        fi[v] = nval;
        seg.update_cnt(0, n + 1, fi[v] - 1, 1, -cnt[v]);
        tag[v] = nval;
        return;
      }
    }
    pushdown(v);
    int mid = (l + r) >> 1;
    if (ql <= mid) update(l, mid, ql, qr, nval, v << 1);
    if (qr > mid) update(mid + 1, r, ql, qr, nval, v << 1 | 1);
    pushup(v);
  }
  void set(int l, int r, int x, int val, int v) {
    if (l == r) {
      seg.update_cnt(0, n + 1, fi[v] - 1, 1, +cnt[v]);
      fi[v] = val;
      seg.update_cnt(0, n + 1, fi[v] - 1, 1, -cnt[v]);
      cnt[v] = 1;
      tag[v] = 0;
      return;
    }
    pushdown(v);
    int mid = (l + r) >> 1;
    if (x <= mid)
      set(l, mid, x, val, v << 1);
    else
      set(mid + 1, r, x, val, v << 1 | 1);
    pushup(v);
  }
} segl;
struct segtree_min {
  int fi[maxn << 2], se[maxn << 2], tag[maxn << 2];
  int cnt[maxn << 2];
  void pushup(int v) {
    fi[v] = max(fi[v << 1], fi[v << 1 | 1]);
    if (fi[v << 1] == fi[v << 1 | 1]) {
      cnt[v] = cnt[v << 1] + cnt[v << 1 | 1];
      se[v] = max(se[v << 1], se[v << 1 | 1]);
    } else if (fi[v << 1] > fi[v << 1 | 1]) {
      cnt[v] = cnt[v << 1];
      se[v] = max(fi[v << 1 | 1], se[v << 1]);
    } else {
      cnt[v] = cnt[v << 1 | 1];
      se[v] = max(fi[v << 1], se[v << 1 | 1]);
    }
  }
  void pushdown(int v) {
    if (tag[v]) {
      if (tag[v] < fi[v << 1]) {
        fi[v << 1] = tag[v << 1] = tag[v];
      }
      if (tag[v] < fi[v << 1 | 1]) {
        fi[v << 1 | 1] = tag[v << 1 | 1] = tag[v];
      }
      tag[v] = 0;
    }
  }
  void init(int l, int r, int v = 1) {
    if (l == r) {
      fi[v] = 0;
      se[v] = INT_MIN;
      cnt[v] = 1;
      return;
    }
    int mid = (l + r) >> 1;
    init(l, mid, v << 1);
    init(mid + 1, r, v << 1 | 1);
    pushup(v);
  }
  void update(int l, int r, int ql, int qr, int nval, int v) {
    if (ql > qr || ql > r || l > qr || nval >= fi[v]) return;
    if (ql <= l && r <= qr) {
      if (nval > se[v]) {
        seg.update_cnt(0, n + 1, fi[v], 1, -cnt[v]);
        fi[v] = nval;
        seg.update_cnt(0, n + 1, fi[v], 1, +cnt[v]);
        tag[v] = nval;
        return;
      }
    }
    pushdown(v);
    int mid = (l + r) >> 1;
    if (ql <= mid) update(l, mid, ql, qr, nval, v << 1);
    if (qr > mid) update(mid + 1, r, ql, qr, nval, v << 1 | 1);
    pushup(v);
  }
  void set(int l, int r, int x, int val, int v) {
    if (l == r) {
      seg.update_cnt(0, n + 1, fi[v], 1, -cnt[v]);
      fi[v] = val;
      seg.update_cnt(0, n + 1, fi[v], 1, +cnt[v]);
      cnt[v] = 1;
      tag[v] = 0;
      return;
    }
    pushdown(v);
    int mid = (l + r) >> 1;
    if (x <= mid)
      set(l, mid, x, val, v << 1);
    else
      set(mid + 1, r, x, val, v << 1 | 1);
    pushup(v);
  }
} segr;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &a[i]);
    pos[a[i]] = i;
  }
  segr.init(1, n);
  segl.init(1, n);
  seg.update_cnt(0, n + 1, 0, 1, -n);
  seg.update_cnt(0, n + 1, n + 1, 1, n);
  for (int i = 1; i <= n; ++i) {
    segr.update(1, n, 1, pos[i] - 1, pos[i] - 1, 1);
    segl.update(1, n, pos[i] + 1, n, pos[i] + 1, 1);
    segl.set(1, n, pos[i], 1, 1);
    segr.set(1, n, pos[i], n, 1);
    seg.update_val(0, n + 1, pos[i], n, 1);
    printf("%lld\n", seg.get_val(1));
  }
  return 0;
}
