/**
* @verified https://atcoder.jp/contests/practice2/tasks/practice2_j
*/
class SegTree {
final int MAX;
final int N;
final java.util.function.BinaryOperator op;
final S E;
final S[] data;
@SuppressWarnings("unchecked")
public SegTree(int n, java.util.function.BinaryOperator op, S e) {
this.MAX = n;
int k = 1;
while (k < n) k <<= 1;
this.N = k;
this.E = e;
this.op = op;
this.data = (S[]) new Object[N << 1];
java.util.Arrays.fill(data, E);
}
public SegTree(S[] dat, java.util.function.BinaryOperator op, S e) {
this(dat.length, op, e);
build(dat);
}
private void build(S[] dat) {
int l = dat.length;
System.arraycopy(dat, 0, data, N, l);
for (int i = N - 1; i > 0; i--) {
data[i] = op.apply(data[i << 1 | 0], data[i << 1 | 1]);
}
}
public void set(int p, S x) {
exclusiveRangeCheck(p);
data[p += N] = x;
p >>= 1;
while (p > 0) {
data[p] = op.apply(data[p << 1 | 0], data[p << 1 | 1]);
p >>= 1;
}
}
public S get(int p) {
exclusiveRangeCheck(p);
return data[p + N];
}
public S prod(int l, int r) {
if (l > r) {
throw new IllegalArgumentException(
String.format("Invalid range: [%d, %d)", l, r)
);
}
inclusiveRangeCheck(l);
inclusiveRangeCheck(r);
S sumLeft = E;
S sumRight = E;
l += N; r += N;
while (l < r) {
if ((l & 1) == 1) sumLeft = op.apply(sumLeft, data[l++]);
if ((r & 1) == 1) sumRight = op.apply(data[--r], sumRight);
l >>= 1; r >>= 1;
}
return op.apply(sumLeft, sumRight);
}
public S allProd() {
return data[1];
}
public int maxRight(int l, java.util.function.Predicate f) {
inclusiveRangeCheck(l);
if (!f.test(E)) {
throw new IllegalArgumentException("Identity element must satisfy the condition.");
}
if (l == MAX) return MAX;
l += N;
S sum = E;
do {
l >>= Integer.numberOfTrailingZeros(l);
if (!f.test(op.apply(sum, data[l]))) {
while (l < N) {
l = l << 1;
if (f.test(op.apply(sum, data[l]))) {
sum = op.apply(sum, data[l]);
l++;
}
}
return l - N;
}
sum = op.apply(sum, data[l]);
l++;
} while ((l & -l) != l);
return MAX;
}
public int minLeft(int r, java.util.function.Predicate f) {
inclusiveRangeCheck(r);
if (!f.test(E)) {
throw new IllegalArgumentException("Identity element must satisfy the condition.");
}
if (r == 0) return 0;
r += N;
S sum = E;
do {
r--;
while (r > 1 && (r & 1) == 1) r >>= 1;
if (!f.test(op.apply(data[r], sum))) {
while (r < N) {
r = r << 1 | 1;
if (f.test(op.apply(data[r], sum))) {
sum = op.apply(data[r], sum);
r--;
}
}
return r + 1 - N;
}
sum = op.apply(data[r], sum);
} while ((r & -r) != r);
return 0;
}
private void exclusiveRangeCheck(int p) {
if (p < 0 || p >= MAX) {
throw new IndexOutOfBoundsException(
String.format("Index %d out of bounds for the range [%d, %d).", p, 0, MAX)
);
}
}
private void inclusiveRangeCheck(int p) {
if (p < 0 || p > MAX) {
throw new IndexOutOfBoundsException(
String.format("Index %d out of bounds for the range [%d, %d].", p, 0, MAX)
);
}
}
// **************** DEBUG **************** //
private int indent = 6;
public void setIndent(int newIndent) {
this.indent = newIndent;
}
@Override
public String toString() {
return toSimpleString();
}
public String toDetailedString() {
return toDetailedString(1, 0);
}
private String toDetailedString(int k, int sp) {
if (k >= N) return indent(sp) + data[k];
String s = "";
s += toDetailedString(k << 1 | 1, sp + indent);
s += "\n";
s += indent(sp) + data[k];
s += "\n";
s += toDetailedString(k << 1 | 0, sp + indent);
return s;
}
private static String indent(int n) {
StringBuilder sb = new StringBuilder();
while (n --> 0) sb.append(' ');
return sb.toString();
}
public String toSimpleString() {
StringBuilder sb = new StringBuilder();
sb.append('[');
for (int i = 0; i < N; i++) {
sb.append(data[i + N]);
if (i < N - 1) sb.append(',').append(' ');
}
sb.append(']');
return sb.toString();
}
}