package contest210129; import java.io.*; import java.util.ArrayDeque; import java.util.Arrays; import java.util.InputMismatchException; import java.util.Queue; public class F3 { InputStream is; FastWriter out; String INPUT = ""; long l(int a, int b) { return (long)a<<32|b; } public void solve() { int n = ni(); int[] a = na(n); Datum[] ds = new Datum[n]; for(int i = 0;i < n;i++){ long[] rs = {1L<<32|n+1}; for(int j = Math.max(i-2, 0);j <= i && j+2 < n;j++){ if(i-j == 0){ if(a[j] > a[j+1]) { // rs = and(rs, new int[][]{{a[j+1]+1, a[j+2]}, {a[j+2]+1, n+1}}); rs = and(rs, new long[]{l(a[j+1]+1, a[j+2]), l(a[j+2]+1, n+1)}); }else{ rs = and(rs, new long[]{l(1, a[j+2]), l(a[j+2]+1, a[j+1])}); // rs = and(rs, new int[][]{{1, a[j+2]}, {a[j+2]+1, a[j+1]}}); } }else if(i-j == 1){ // rs = and(rs, new int[][]{{1, Math.min(a[j], a[j+2])}, {Math.max(a[j], a[j+2])+1, n+1}}); rs = and(rs, new long[]{l(1, Math.min(a[j], a[j+2])), l(Math.max(a[j], a[j+2])+1, n+1)}); }else if(i-j == 2){ if(a[j] > a[j+1]) { rs = and(rs, new long[]{l(a[j+1]+1, a[j]), l(a[j]+1, n+1)}); }else{ rs = and(rs, new long[]{l(1, a[j]), l(a[j]+1, a[j+1])}); } } } ds[i] = new Datum(rs, a[i]); } long ans = dfs(0, n, ds); for(int i = 0;i < n;i++){ for(int j = i+1;j <= i+2 && j < n;j++){ {int d = a[i]; a[i] = a[j]; a[j] = d;} boolean ok = true; for(int k = Math.max(0, i-2);k <= j && k+2 < n;k++){ if(!kdmt(a[k], a[k+1], a[k+2]))ok = false; } if(ok){ ans++; } {int d = a[i]; a[i] = a[j]; a[j] = d;} } } out.println(ans); } static class Datum { long[] rs; int v; public Datum(long[] rs, int v) { this.rs = rs; this.v = v; } } int[] ft = new int[200004]; Datum[] temp = new Datum[200004]; long dfs(int l, int r, Datum[] ds) { if (r - l <= 3) { Arrays.sort(ds, l, r, (x, y) -> x.v - y.v); return 0L; } int h = l + r >> 1; long ret = 0; for (int i = Math.max(l, h - 2); i < h; i++) { for (int j = h; j < h + 2 && j < r; j++) { if (j - i <= 2) { Datum L = ds[i], R = ds[j]; if (isin(R.v, L.rs) && isin(L.v, R.rs)) { ret--; } } } } ret += dfs(l, h, ds) + dfs(h, r, ds); int pp = 0; for(int i = h;i < r;i++){ long[] tar = ds[i].rs; pp += 2*tar.length; } long[] es = new long[pp]; int p = 0; for(int i = h;i < r;i++){ long[] tar = ds[i].rs; for(long t : tar){ es[p++] = t>>>32<<32|ds[i].v<<1|0; es[p++] = (long)((int)t)<<32|ds[i].v<<1|1; } } Arrays.sort(es); // int[][] es = new int[pp][]; // int p = 0; // for(int i = h;i < r;i++){ // int[][] tar = ds[i].rs; // for(int[] t : tar){ // es[p++] = new int[]{t[0], ds[i].v, -1}; // es[p++] = new int[]{t[1], ds[i].v, 1}; // } // } // Arrays.sort(es, (x, y) -> x[0] - y[0]); int q = 0; for(long e : es){ while(q < h-l && ds[q+l].v < e>>>32){ for(long u : ds[q+l].rs){ addFenwick(ft, (int)(u>>>32), (int)u, 1); } q++; } ret += ((e&1)*2-1) * sumFenwick(ft, ((int)e)>>>1); } while(q > 0){ for(long u : ds[q-1+l].rs){ addFenwick(ft, (int)(u>>>32), (int)u, -1); } q--; } { for (int i = l; i < r; i++) { temp[i] = ds[i]; } int i = l, j = h, o = l; for (; i < h && j < r; ) { if (ds[i].v <= ds[j].v) { ds[o++] = temp[i++]; } else { ds[o++] = temp[j++]; } } while (i < h) ds[o++] = temp[i++]; while (j < r) ds[o++] = temp[j++]; } return ret; } boolean isin(int x, long[] rs) { for(long r : rs){ if(r>>>32 <= x && x < (int)r)return true; } return false; } public static int sumFenwick(int[] ft, int i) { int sum = 0; for(i++;i > 0;i -= i&-i)sum += ft[i]; return sum; } public static void addFenwick(int[] ft, int l, int r, int v) { addFenwick(ft, l, v); addFenwick(ft, r, -v); } public static void addFenwick(int[] ft, int i, int v) { if(v == 0 || i < 0)return; int n = ft.length; for(i++;i < n;i += i&-i)ft[i] += v; } public static int lowerBound(int[] a, int v){ return lowerBound(a, 0, a.length, v); } public static int lowerBound(int[] a, int l, int r, int v) { if(l > r || l < 0 || r > a.length)throw new IllegalArgumentException(); int low = l-1, high = r; while(high-low > 1){ int h = high+low>>>1; if(a[h] >= v){ high = h; }else{ low = h; } } return high; } public static long[] and(long[] a, long[] b) { long[] rs = new long[a.length + b.length]; int p = 0; for(int i = 0, j = 0;i < a.length && j < b.length;){ long from = Math.max(a[i]>>>32, b[j]>>>32); long to = Math.min((int)a[i], (int)b[j]); if(from < to)rs[p++] = from<<32|to; if((int)a[i] < (int)b[j]){ i++; }else{ j++; } } return Arrays.copyOf(rs, p); } boolean kdmt(int[] a) { int n = a.length; for(int i = 0;i < n-2;i++){ if(!kdmt(a[i], a[i+1], a[i+2])){ return false; } } return true; } boolean kdmt(int a, int b, int c) { if(a == b)return false; if(c == b)return false; if(a == c)return false; return a < b && b > c || a > b && b < c; } public static void main(String[] args) { new F3().run(); } public void run() { // int n = 200000, m = 99999; // Random gen = new Random(); // StringBuilder sb = new StringBuilder(); // sb.append(n + " "); // for (int i = 0; i < n; i++) { // sb.append((i % 2 == 0 ? i/2+1 : i/2+n/2+1) + " "); // } // INPUT = sb.toString(); long S = System.currentTimeMillis(); is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new FastWriter(System.out); solve(); out.flush(); long G = System.currentTimeMillis(); tr(G-S+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } private boolean eof() { if(lenbuf == -1)return true; int lptr = ptrbuf; while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false; try { is.mark(1000); while(true){ int b = is.read(); if(b == -1){ is.reset(); return true; }else if(!isSpaceChar(b)){ is.reset(); return false; } } } catch (IOException e) { return true; } } private final byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } // private boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private int ni() { int num = 0, b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } public static class FastWriter { private static final int BUF_SIZE = 1<<13; private final byte[] buf = new byte[BUF_SIZE]; private final OutputStream out; private int ptr = 0; private FastWriter(){out = null;} public FastWriter(OutputStream os) { this.out = os; } public FastWriter(String path) { try { this.out = new FileOutputStream(path); } catch (FileNotFoundException e) { throw new RuntimeException("FastWriter"); } } public FastWriter write(byte b) { buf[ptr++] = b; if(ptr == BUF_SIZE)innerflush(); return this; } public FastWriter write(char c) { return write((byte)c); } public FastWriter write(char[] s) { for(char c : s){ buf[ptr++] = (byte)c; if(ptr == BUF_SIZE)innerflush(); } return this; } public FastWriter write(String s) { s.chars().forEach(c -> { buf[ptr++] = (byte)c; if(ptr == BUF_SIZE)innerflush(); }); return this; } private static int countDigits(int l) { if (l >= 1000000000) return 10; if (l >= 100000000) return 9; if (l >= 10000000) return 8; if (l >= 1000000) return 7; if (l >= 100000) return 6; if (l >= 10000) return 5; if (l >= 1000) return 4; if (l >= 100) return 3; if (l >= 10) return 2; return 1; } public FastWriter write(int x) { if(x == Integer.MIN_VALUE){ return write((long)x); } if(ptr + 12 >= BUF_SIZE)innerflush(); if(x < 0){ write((byte)'-'); x = -x; } int d = countDigits(x); for(int i = ptr + d - 1;i >= ptr;i--){ buf[i] = (byte)('0'+x%10); x /= 10; } ptr += d; return this; } private static int countDigits(long l) { if (l >= 1000000000000000000L) return 19; if (l >= 100000000000000000L) return 18; if (l >= 10000000000000000L) return 17; if (l >= 1000000000000000L) return 16; if (l >= 100000000000000L) return 15; if (l >= 10000000000000L) return 14; if (l >= 1000000000000L) return 13; if (l >= 100000000000L) return 12; if (l >= 10000000000L) return 11; if (l >= 1000000000L) return 10; if (l >= 100000000L) return 9; if (l >= 10000000L) return 8; if (l >= 1000000L) return 7; if (l >= 100000L) return 6; if (l >= 10000L) return 5; if (l >= 1000L) return 4; if (l >= 100L) return 3; if (l >= 10L) return 2; return 1; } public FastWriter write(long x) { if(x == Long.MIN_VALUE){ return write("" + x); } if(ptr + 21 >= BUF_SIZE)innerflush(); if(x < 0){ write((byte)'-'); x = -x; } int d = countDigits(x); for(int i = ptr + d - 1;i >= ptr;i--){ buf[i] = (byte)('0'+x%10); x /= 10; } ptr += d; return this; } public FastWriter write(double x, int precision) { if(x < 0){ write('-'); x = -x; } x += Math.pow(10, -precision)/2; // if(x < 0){ x = 0; } write((long)x).write("."); x -= (long)x; for(int i = 0;i < precision;i++){ x *= 10; write((char)('0'+(int)x)); x -= (int)x; } return this; } public FastWriter writeln(char c){ return write(c).writeln(); } public FastWriter writeln(int x){ return write(x).writeln(); } public FastWriter writeln(long x){ return write(x).writeln(); } public FastWriter writeln(double x, int precision){ return write(x, precision).writeln(); } public FastWriter write(int... xs) { boolean first = true; for(int x : xs) { if (!first) write(' '); first = false; write(x); } return this; } public FastWriter write(long... xs) { boolean first = true; for(long x : xs) { if (!first) write(' '); first = false; write(x); } return this; } public FastWriter writeln() { return write((byte)'\n'); } public FastWriter writeln(int... xs) { return write(xs).writeln(); } public FastWriter writeln(long... xs) { return write(xs).writeln(); } public FastWriter writeln(char[] line) { return write(line).writeln(); } public FastWriter writeln(char[]... map) { for(char[] line : map)write(line).writeln(); return this; } public FastWriter writeln(String s) { return write(s).writeln(); } private void innerflush() { try { out.write(buf, 0, ptr); ptr = 0; } catch (IOException e) { throw new RuntimeException("innerflush"); } } public void flush() { innerflush(); try { out.flush(); } catch (IOException e) { throw new RuntimeException("flush"); } } public FastWriter print(byte b) { return write(b); } public FastWriter print(char c) { return write(c); } public FastWriter print(char[] s) { return write(s); } public FastWriter print(String s) { return write(s); } public FastWriter print(int x) { return write(x); } public FastWriter print(long x) { return write(x); } public FastWriter print(double x, int precision) { return write(x, precision); } public FastWriter println(char c){ return writeln(c); } public FastWriter println(int x){ return writeln(x); } public FastWriter println(long x){ return writeln(x); } public FastWriter println(double x, int precision){ return writeln(x, precision); } public FastWriter print(int... xs) { return write(xs); } public FastWriter print(long... xs) { return write(xs); } public FastWriter println(int... xs) { return writeln(xs); } public FastWriter println(long... xs) { return writeln(xs); } public FastWriter println(char[] line) { return writeln(line); } public FastWriter println(char[]... map) { return writeln(map); } public FastWriter println(String s) { return writeln(s); } public FastWriter println() { return writeln(); } } public static void trnz(int... o) { for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" "); System.out.println(); } // print ids which are 1 public static void trt(long... o) { Queue stands = new ArrayDeque<>(); for(int i = 0;i < o.length;i++){ for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x)); } System.out.println(stands); } public static void tf(boolean... r) { for(boolean x : r)System.out.print(x?'#':'.'); System.out.println(); } public static void tf(boolean[]... b) { for(boolean[] r : b) { for(boolean x : r)System.out.print(x?'#':'.'); System.out.println(); } System.out.println(); } public void tf(long[]... b) { if(INPUT.length() != 0) { for (long[] r : b) { for (long x : r) { for (int i = 0; i < 64; i++) { System.out.print(x << ~i < 0 ? '#' : '.'); } } System.out.println(); } System.out.println(); } } public void tf(long... b) { if(INPUT.length() != 0) { for (long x : b) { for (int i = 0; i < 64; i++) { System.out.print(x << ~i < 0 ? '#' : '.'); } } System.out.println(); } } private void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); } }