import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } void bAdd(T)(T[] bit, int pos, T val) in { assert(0 <= pos && pos < bit.length, "bAdd: 0 <= pos < |bit| must hold"); } do { for (int x = pos; x < bit.length; x |= x + 1) { bit[x] += val; } } // sum of [0, pos) T bSum(T)(T[] bit, int pos) in { assert(0 <= pos && pos <= bit.length, "bSum: 0 <= pos <= |bit| must hold"); } do { T ret = 0; for (int x = pos - 1; x >= 0; x = (x & (x + 1)) - 1) { ret += bit[x]; } return ret; } enum INF = 10^^9; void main() { try { for (; ; ) { const N = readInt; auto P = new int[N]; foreach (i; 0 .. N) { P[i] = readInt - 1; } auto score = new int[][](N + 1, N + 1); { auto bit = new int[N]; foreach (i; 0 .. N) { bit[] = 0; foreach (j; i .. N) { score[i][j + 1] = score[i][j] + ((j - i) - bit.bSum(P[j])); bit.bAdd(P[j], 1); } } } debug { writeln("score = ", score); } auto dp = new int[][](N + 1, N + 1); foreach (k; 0 .. N + 1) { dp[k][] = -INF; } dp[0][0] = 0; int len; auto que = new int[N + 1]; foreach (k; 0 .. N) { len = 0; foreach (i; 0 .. N + 1) { int calc(int j) { return dp[k][j] + score[j][i]; } bool check(int j2, int j1) { int lo = i, hi = N + 1; for (; lo + 1 < hi; ) { const mid = (lo + hi) / 2; ((dp[k][j1] + score[j1][mid] >= dp[k][i] + score[i][mid]) ? hi : lo) = mid; } return (hi > N || dp[k][j2] + score[j2][hi] >= dp[k][j1] + score[j1][hi]); } for (; len >= 2 && calc(que[len - 2]) >= calc(que[len - 1]); --len) {} if (len >= 1) { dp[k + 1][i] = calc(que[len - 1]); } if (len == 0 || calc(que[len - 1]) < calc(i)) { for (; len >= 2 && check(que[len - 2], que[len - 1]); --len) {} que[len++] = i; } } debug { writefln("dp[%s] = %s", k + 1, dp[k + 1]); } } foreach (k; 1 .. N + 1) { writeln(score[0][N] - dp[k][N]); } } } catch (EOFException e) { } }