struct segment_tree{
    struct node{
        int val;
        node* left = NULL, * right = NULL;
        node(int v):val(v){}
        void update() { val = max(left->val, right->val); }
        node(node* a, node* b){
            val = max(a->val, b->val);
            left = a, right = b;
        }
    };
    node* root;
    node* init(int l, int r, int* v){
        if(l == r)return new node(v[l]);
        int m = l + r >> 1;
        return new node(init(l, m, v), init(m+1, r, v));
    }
    void modify(int pos, int nv, node* now, int l = 1, int r = n){
        if(l == r) return now->val = nv, void();
        if(pos > r || pos < l)return;
        int m = l + r >> 1;
        modify(pos, nv, now->left, l, m);
        modify(pos, nv, now->right, m+1, r);
        now->update();
    }
    int query(int ql, int qr, node* now, int l = 1, int r = n){
        if(ql > r || qr < l) return -(1 << 29);
        if(ql <= l && r <= qr) return now->val;
        int m = l + r >> 1;
        return max(query(ql, qr, now->left, l, m),
                query(ql, qr, now->right, m+1, r));
    }
};
 

const int maxn = 1 << 20;
const int inf = 1 << 29;
struct segment_tree{
    int max_val[maxn << 1];
    void modify(int pos, int new_val, int l = 1, int r = n, int i = 1){
        if (l > pos || r < pos) return;
        if (l == r) return max_val[i] = new_val, void();
        int m = l + r >> 1;
        modify(pos, new_val, l, m, i<<1);
        modify(pos, new_val, m+1, r, i<<1|1);
        max_val[i] = max(max_val[i<<1], max_val[i<<1|1]);
    }
    int query_max(int ql, int qr, int l = 1, int r = n, int i = 1) {
        if (ql > r || qr < l) return -inf;
        if (ql <= l && qr >= r) return max_val[i];
        int m = l + r >> 1;
        return max(query_max(ql, qr, l, m, i<<1),
        		query_max(ql, qr, m+1, r, i<<1|1);
    }
};

struct bit {
    int v[maxn];
    void add(int i, int val) {
        for (;i <= n;i += i&-i)
            v[i] += val;
    }
    int query(int i) {
        int res = 0;
        for (;i;i ^= i&-i)
            res += v[i];
        return res;
    }
}tree;