Vasya has an array of n integers a_1, a_2, …, a_n. Vasya thinks that all numbers in his array are strange for some reason. To calculate how strange the i-th number is, Vasya created the following algorithm.

He chooses a subsegment a_l, a_{l+1}, …, a_r, such that 1 ≤ l ≤ i ≤ r ≤ n, sort its elements in increasing order in his head (he can arrange equal elements arbitrary). After that he finds the center of the segment. The center of a segment is the element at position (l + r) / 2, if the length of the segment is odd, and at position (l + r + 1) / 2 otherwise. Now Vasya finds the element that was at position i before the sorting, and calculates the distance between its current position and the center of the subsegment (the distance between the elements with indices j and k is |j - k|).

The strangeness of the number at position i is the maximum distance among all suitable choices of l and r. 

Vasya wants to calculate the strangeness of each number in his array. Help him to do it. 

Input

The first line contains a single integer n (1 ≤ n ≤ 200 000) — the size of the array.

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ n) — Vasya's array.

Output

Print a single line with n numbers. The i-th of them must be equal to the strangeness of the i-th element of the array.

Examples

Input


5
5 4 3 2 1


Output


2 1 1 2 2 


Input


7
3 6 5 6 2 1 3


Output


2 3 1 3 2 3 1 

Note

In the first example:

  1. For the first position we choose the segment from 1 to 5. After sorting, it looks like [1, 2, 3, 4, 5], the center is 3. The distance from the center to 5 is 2.
  2. For the second position we choose the segment from 2 to 4.
  3. For the third position we choose the segment from 3 to 5.
  4. For the fourth position we choose the segment from 1 to 4. After sorting, it looks like [2, 3, 4, 5], the center is 4. The distance from the center to 2 is 2. 
  5. For the fifth position we choose the segment from 1 to 5.
#include<bits/stdc++.h>
#define ll long long
#define pb push_back
#define lowbit(x) ((x)&(-(x)))
#define mid ((l+r)>>1)
#define lson rt<<1, l, mid
#define rson rt<<1|1, mid+1, r
#define fors(i, a, b) for(int i = (a); i < (b); ++i)
#define all(vec) vec.begin(),vec.end()
using namespace std;
const int maxn = 2e5 + 5;
const int inf = 0x3f3f3f3f;
namespace seg{
    int mx[maxn<<2], mi[maxn<<2], lz[maxn<<2];
    void up(int rt){
        mx[rt] = max(mx[rt<<1], mx[rt<<1|1]);
        mi[rt] = min(mi[rt<<1], mi[rt<<1|1]);
    }
    void down(int rt){
        lz[rt<<1] += lz[rt]; mi[rt<<1] += lz[rt]; mx[rt<<1] += lz[rt];
        lz[rt<<1|1] += lz[rt]; mi[rt<<1|1] += lz[rt]; mx[rt<<1|1] += lz[rt];
        lz[rt] = 0;
    }
    void rebuild(int rt, int l, int r){
        lz[rt] = mi[rt] = mx[rt] = 0;
        if(l == r){
            mx[rt] = mi[rt] = -l; return;
        }
        rebuild(lson); rebuild(rson); up(rt); return;
    }
    void update(int rt, int l, int r, int L, int R, int x){
        if(L <= l && r <= R) {
            lz[rt] += x; mi[rt] += x; mx[rt] += x;
            return;
        }down(rt);
        if(L <= mid) update(lson, L, R, x);
        if(R > mid) update(rson, L, R, x);
        up(rt);
    }
    int qry_mi(int rt, int l, int r, int L, int R){
        if(L <= l && r <= R) return mi[rt];
        int res = inf;
        down(rt);
        if(L <= mid) res = min(res, qry_mi(lson, L, R));
        if(R > mid) res = min(res, qry_mi(rson, L, R));
        return res;
    }
    int qry_mx(int rt, int l, int r, int L, int R){
        if(L <= l && r <= R) return mx[rt];
        int res = -inf;
        down(rt);
        if(L <= mid) res = max(res, qry_mx(lson, L, R));
        if(R > mid) res = max(res, qry_mx(rson, L, R));
        return res;
    }
}
using namespace seg;
int a[maxn], n;
vector<int> pos[maxn];
int ans[maxn];
int main()
{
    scanf("%d", &n);
    fors(i,1,n+1) scanf("%d", &a[i]), pos[a[i]].pb(i);

    rebuild(1, 0, n);

    fors(i,1,n+1){
        for(int x:pos[i]) update(1, 0, n, x, n, 2);

        for(int x:pos[i]){
            int sr = qry_mx(1, 0, n, x, n);
            int sl = qry_mi(1, 0, n, 0, x-1);

            ans[x] = max(ans[x], (sr-sl+1)/2-1 );
        }
    }
    rebuild(1, 0, n);

    for(int i = n; i > 0; --i){
        for(int x:pos[i]) update(1, 0, n, x, n, 2);
        for(int x:pos[i]){
            int sr = qry_mx(1, 0, n, x, n);
            int sl = qry_mi(1, 0, n, 0, x-1);
            ans[x] = max(ans[x], (sr-sl)/2);
        }
    }
    fors(i,1,n+1) printf("%d ", ans[i]);
	return 0;
}
