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/**

* @verified https://atcoder.jp/contests/practice2/tasks/practice2_j

*/

class SegTree<S> {

final int MAX;

final int N;

final java.util.function.BinaryOperator<S> op;

final S E;

final S[] data;

@SuppressWarnings("unchecked")

public SegTree(int n, java.util.function.BinaryOperator<S> 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<S> 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<S> 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<S> 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();

}

}