Rust trait constraints. You can only require the types to implement a number of traits. Moreover, the types which implement the trait might not have a reflexive AsRef implementation, such as i32. More Explanation. trait GameState: std::marker::Sized + Debug { type G: Game; fn generate_children(&self, game: &Self::G) -> Vec<Self>; fn get_initial_state(game: &Self::G) -> Self; } // note: now G is given by the GameState implementation instead of // being a Feb 18, 2021 · How can we overcome the problem of associated type defaults when we need a type that depends on other type in a trait? trait Foo{ type C; type K = Vec&lt;Self::C&gt;; } error[ PartialOrd and Display are traits. However, Rust discourages it in favor of static type checks. Generally functions that work with any integer types will be super tedious to specify, as you will have to require everything from std::ops and their outputs. NumAssign The trait for Num types which also implement assignment operators. In any other case, the inherent impl fails, so we get the fallback blanket implementation which gives false. Ask Question Asked 6 years, 8 months ago. Note: Traits are similar to a feature often called interfaces in other languages, although with some differences. A trait can have multiple implementations for different input types. T-lang Relevant to the language team, which will review and decide on the PR/issue. What is a Trait? In Rust, data types - primitives, structs, enums and any other ‘aggregate’ types like tuples and arrays - are dumb. Expand impl Trait to allow use in arguments, where it behaves like an anonymous generic parameter. We can express the behavior of generics or how they relate to other generics without knowing what will be in their place Mar 8, 2023 · Removing the constraint where T: Permission<Execute = Allow> will open the door back for s1. Furthermore, if Item is a type parameter, then Item::Assoc can be used in type parameters. Jun 17, 2017 · A-specialization Area: Trait impl specialization A-traits Area: Trait system C-feature-request Category: A feature request, i. When applied to constness, it means that a trait function could be const in the impl but not in Sep 19, 2023 · The where clause in Rust allows you to specify constraints on items like functions, impl blocks, traits, types, etc. } I became extremely confused when I Sep 9, 2019 · Rust use macros for long Trait constraint chains. Core concepts. In this thesis, we present MiniRust—a formal model of a subset of Rust. Every programming language has tools for effectively handling the duplication of concepts. The required trait is a supertrait of the trait we’re implementing. @taufik-rama's solution of requiring a getter function is the way you can require something like a field. types implementing the trait also expose the necessary behavior, and 2. This reminded me of the recently accepted RFC: Overconstraining and omitting unsafe in impls of unsafe trait methods. a trait can only be implemented to a type if either the trait or the type or both are in your current crate) would still not limit anyone to A trait object is an opaque value of another type that implements a set of traits. Traits can be implemented for any data type. Right now the only way to ensure that the closure is size zero is to try to transmute it Mar 21, 2016 · To fix this, we need to have our trait be aware that you can only decode_from certain lifetimes, not arbitrary ones. Also, you can't use a type as T if it doesn't implement SomeTrait , so I'm not sure what your concern in this case is. I'd like to write a function (build_with_42_for_bool<Builder>) that constraints the Builder to only th Feb 25, 2021 · A where clause specifies constraints on some generic code element---a function, type, trait, or in this case, implementation---based on the traits and lifetimes that one or more generic parameters, or a derivative thereof, must satisfy. The use of "Associated types" improves the overall readability of code by moving inner types locally into a trait as output types. Think about natural language: I've never seen a purple elephant, but I can easily name the concept of "purple elephant We can use traits to define shared behavior in an abstract way. Jul 1, 2024 · AFAIK in Rust, trait generics are strictly more powerful than associated types, so if you can do something with associated types, the same thing should be possible with generics (but possibly in a less ergonomic way). But closure types are deprecated in favor of traits and object types as part of RFC #44 (unboxed closures). In both cases those are bounds: Trait: Sized states that the trait itself can only be implemented for a type that already implements Aug 15, 2021 · If you want to use any methods or constants coming from T, then T must be bounded/constrained by some trait, because you can use only methods/constants/etc coming from the trait bounds. "B impls some trait [that takes A as a generic argument]" The Rust Programming Language Forum Nov 27, 2017 · impl Traits as function arguments are desugared to an anonymous generic parameter. type Output = [i32; N]; } } #![allow(unused)] fn main() { // Examples where const generic parameters cannot be used. I'd like to imple Feb 6, 2022 · The RangeIndex<T> trait puts the constraints I need on the index type, Rust doesn't complain about this, since Wrapper is a type from this crate. 52k 104 104 gold badges 299 299 silver badges 466 Jun 11, 2019 · Even if you would define a trait in an external crate and implement the behaviour for specific types only in that external crate, thinking that the trait implementation rules will help you there (i. type Node: Node<Edge = Self::Edge>; type Edge: Edge<Node = Self::Node>; fn get_nodes(&self) -> Vec<Self::Node>; Sep 6, 2022 · Leverages the generics capabilities provided by Rust that solve this particular problem; Follow the best practices of the Rust community by using ‘trait bounds’ and generics; Significantly more succint in the approach, as the comparison table above proved; Uses the expressing power of Rust effectively. May 21, 2017 · What is the difference between Trait: Sized and where Self: Sized? (Well, yes, one inherits the trait the other one is a parameter bound, but from Rust's trait object perspective?) There is no inheritance in Rust. You might also see it called a constraint . Dec 31, 2020 · In Rust we call the things that define ranges of values "type", u8 and Vec<f32> are types. The model focuses on the trait system and includes some advanced features of traits such as associated types and trait objects. For example, the following example uses the trait Display to print and so it requires T to be bound by Display; that is, T must implement Display. Jun 17, 2016 · For anyone still curious about this as of Rust 1. Jun 29, 2018 · trait A {} trait B {} trait C {} struct D<T, X> where if T: A then X: is not B else if X: B then T: C {} I've already found some way to bypass this, but I want a way to do it with language features. What would the non-trait versions of save() and restore() look like for SimpleKeeper<'a>? Very similar, actually. There's not really a general workaround beyond "do something else" which would typically look like an inherent conversion method, using a different (custom) trait, or allowing another mechanism for users to access the inner values and do the conversion themselves. The goal of the trait system is to check whether a given trait bound is satisfied. Putting a bound on the type itself imposes a more abstract constraint, that it's actually impossible to express the idea of a type that doesn't hold those Dec 17, 2014 · Rust is not dynamically typed; the way you've written SomeStruct means it cannot support values of multiple types. method(); // Dynamic dispatch. Instead, you can create a new trait with the traits you want as super traits and provide a blanket implementation: Nov 7, 2021 · Note that the original type constraints must still be replicated on both the trait definition and the implementation, to ensure that 1. The RFC introducing where contains detailed information about the keyword. Modified 6 years, 7 months ago. But we’ll use T because, by convention, type parameter names in Rust are short, often just one letter, and Rust’s type-naming convention is UpperCamelCase. I'd like to extract this idea into its own RFC. If a type Item has an associated type Assoc from a trait Trait, then <Item as Trait>::Assoc is a type that is an alias of the type specified in the associated type definition. For example, imagine a function that takes two references with different lifetimes and returns a reference with a lifetime that is a sub-lifetime of both inputs. §Examples. This requires support Nov 24, 2016 · One advantage of making a new type over implementing a new trait for existing types is that you can add foreign traits and inherent behavior to the new type. constraints ([Constraint:: Trait Implementations. Short for type, T is the default choice of most Rust programmers. . The greatest difference between Concepts and Traits is that Concepts use structural typing whereas Traits use nominal typing: Sep 30, 2014 · Today, the Add trait is defined using only single-dispatch (like so): pub trait Add<Rhs,Sum> { fn add(&self, rhs: &Rhs) -> Sum; } The expression a + b is thus sugar for Add::add(&a, &b). I can make my own trait combining these constraints, like this: trait LongNumValue: Integer + MulAssign + CheckedMul + CheckedAdd + Copy + From<u8> {} struct LongNum<T: LongNumValue> { values: Vec<T>, powers: Vec<u8>, radix: u8, } Jan 20, 2015 · Unfortunately, what you want to do is inexpressible in Rust at the moment. Whitelist vs blacklist problem. Viewed 517 times May 20, 2015 · pub trait BorrowMut<Borrowed>: Borrow<Borrowed> where Borrowed: ?Sized, { fn borrow_mut(&mut self) -> &mut Borrowed; } What does the question mark in front of Sized mean in this type parameter bound (Borrowed: ?Sized)? I consulted: The Rust Programming Language¹ book, The Rust Reference², and also Nov 23, 2023 · Marker traits are already in Rust, refinement types and contracts are possible with experimental libraries. impl<'a> Decode<'a, MQTTFrame<'a>> for MQTTFrameDecoder<'a> { for<'a> can be read as "for all choices of 'a", and basically produces an infinite list of trait bounds that F must satisfy. Vertical) . Manually add a marker trait for types where the runtime constraint is met. In the value case, there's a single type T used, and all constraints are defined These constraints cannot be expressed by users, but they arise from impl Trait due to its lifetime capture rules. Sep 8, 2018 • Steve Donovan. If only some instances of a particular type satisfy the constraint, create a type-safe wrapper. You will choose between storing a trait object or a struct of a concrete type whether you want that the same instance of Test is able to own a struct of changing types (all implementing the specified trait) or if a specific instance of Test is tied to a concrete type T. Sep 9, 2021 · One possibility is like that Playground. This interface consists of associated items, which come in three varieties: functions; types; constants; All traits define an implicit type parameter Self that refers to "the type that is implementing this interface". In Rust, one such tool is generics: abstract stand-ins for concrete types or other properties. Aug 30, 2021 · There are currently discussions how to use traits in const contexts. Bounds. e. fn use_container<C: Container>(c: C) where C: Clone, C::ValueType: Clone { let _ = c. Generic traits take types as "input", while associated types are a kind of "output" type. But such a feature is not something that can be easily outlined for implementation into the language, nor do I know of an RFC I am writting some generic functions in Rust and was wondering if there is a way to implement a custom trait constraint (restriction) on the generic type that would inherit the traits the underlying stucts derivce. Type mismatch with iterator of traits as function argument. r. The important part is that the struct stores the reference itself, so it needs to have a lifetime parameter for the values inside. Feel free to also look at the docs for the current solver and the chalk solver can be found separately. source impl Clone for Layout. Nov 6, 2023 · It seems like you understand why a trait cannot have an associated type or constant in order to be object safe. Generic Types, Traits, and Lifetimes. Nov 4, 2015 · In Graph 's definition, you can constrain each associated type's associated type (!) to be equal to the corresponding associated type in Graph. In some cases you may use the type-safe wrapper and Apr 9, 2022 · Conditionally implement a Rust trait only if a type constraint is satisfied. Intense. Mar 12, 2021 · For example, I have the following trait trait Foo { const FOO: usize; } And how to write constraint to make sure FOO is less than 4? The following code does not compile: fn foo<T: Foo>() where <T as Foo>::FOO < 4 {} A trait describes an abstract interface that types can implement. When working with generics, the type parameters often must use traits as bounds to stipulate what functionality a type implements. We can use trait bounds to specify that a generic type can be any type that has certain behavior. This concept is called over-constraining because it allows trait impls to have more constraints than the trait. Oct 4, 2022 · No, it is not possible to exclude specific types in a generic implementation. Structural vs Nominal. You can use any identifier as a type parameter name. Trait objects implement the base trait, its auto traits, and any supertraits of the base trait. g. There's no way to require a field be present on a type implementing a trait. They may have methods but that is just a convenience (they are just functions). There aren't many places outside of the Fn traits where we encounter HRTBs, and even for those we have a nice magic sugar for the common cases. where allows specifying constraints on lifetime and generic parameters. For example: // Declares a new item `Foo` with kind `type -> constraint` trait Foo { } // T: Foo applies Foo to `T`, `(type -> constraint)(type) => constraint` fn bar < T > ( ) where T : Foo { } May 15, 2019 · Rust Traits are used both for Compile-Time Polymorphism and, sometimes, Run-Time Polymorphism; Concepts are only about Compile-Time Polymorphism. For example, the following defines the type Point as a synonym for the type (u8, u8), the type of pairs of unsigned 8 bit integers: Jan 23, 2020 · Currently all of the generic story with primitive numeric types in Rust is available in the official num crate. We can use traits to define shared behavior in an abstract way. It has been discussed how to implement an alias but it was decided that it wasn't needed. There are also shorter forms for certain common cases: Bounds written after declaring a generic parameter: fn f<A: Copy>() {} is the same as fn f<A>() where A: Copy {}. They can access other methods declared in the same trait. Dec 30, 2021 · I have a type Builder with a Generic Associated Type (GAT) InstanceForBuilder<'a>. The struct Vec<T> { } is sometimes called "type", but it is a "type constructor" instead. For example a trait may be constrained to only be implemented by types which implement another trait. at. You can see how the crate implements the trait here: Oct 31, 2018 · trait Trait<T> { fn method(&self) -> T; } impl Trait<u8> for Struct { fn method(&self) -> u8 { 16 } } You use the "associated type" way when there is only one logical form of the trait to use. Add constraints that must be upheld to use an item. that type, and a blanket impl of a trait for a type (satisfying another trait) also means to bound the trait being implemented, although in the opposite Trait solving (new) This chapter describes how trait solving works with the new WIP solver located in rustc_trait_selection/solve. Because of how our trait system works, this means that only the type of the left-hand side (the Self parameter) will be Apr 8, 2019 · The problem is that I need to repeat this verbose constraint for T in all impls. Note however that with the current approach you can have only one constraint per type a trait can be thought of as a type operator generating a "constraint" - what in Rust would usually be called a bound. In your case that would be: pub trait FromLeBytes { const BITS: u32; fn from_le_bytes(bytes: [u8; 4]) -> Self; } That part doesn't have a name by itself (I don't think), but T::Item: ToString is called a bound, or a trait bound. Aug 8, 2021 · Since this is an impl on IsDebug itself, not on a trait implementation, it takes precedent over the NotDebug blanket implementation. Syntax for the trait definition is as follows: #![allow(unused)] fn main() { // `A` and `B` are defined in the trait via the `type` keyword. Defining a Trait use std::fmt::Debug; trait PrintInOption { fn print_in_option(self); } // Because we would otherwise have to express this as `T: Debug` or // use another method of indirect approach, this requires a `where` clause: impl<T> PrintInOption for T where Option<T>: Debug { // We want `Option<T>: Debug` as our bound because that is what's // being Nov 10, 2021 · Rust doesn't have inheritance. A trait is a collection of methods defined for an unknown type: Self. The signature of Read trait that actually would work is as follows (in pseudo-Rust): trait<'r> Read for Self<'r> { fn read<'a>(mem: &'a [u8]) -> Result<Self<'a>, String>; // ' } That is, Self must be a higher-kinded type in its lifetime parameter. How can I handle this special case? trait MyTrait { } impl<T> MyTrait for Vec<T> /* where T: !u8 */ { } impl MyTrait for Vec<u8> { } results in error[E0119]: conflicting implementations of trait `MyTrait` for type `std::vec::Vec<u8>`: I guess that Tracking issue for specialization (RFC 1210) · Issue #31844 Dec 31, 2017 · Conditionally implement a Rust trait only if a type constraint is satisfied. Aug 30, 2023 · Suppose we have: trait Foo { type A; type B; } Does Rust allow us to express additional constraints, i. A generic trait constraint is a trait that is associated with a generic type parameter, allowing any type to implement the trait as long as it satisfies the constraint. Ask Question Asked 4 years, 11 months ago. This crate contains, among everything else, a number of traits which are implemented for various primitive numeric types, and in particular there is Float which represents a floating-point number. t. When a type implements a trait it can be treated abstractly as that trait using generics or trait objects. In your case the constraint is a lifetime bound. Every value has a single, specific type, but may implement several different traits, or be compatible with several different type constraints. The Animal trait is then implemented for the Sheep data type, allowing the use of methods from Animal Sep 3, 2017 · This is what the num-traits crate can be used for. The base trait for numeric types, covering 0 and 1 values, comparisons, basic numeric operations, and string conversion. Dec 28, 2016 · The idea of a != constraint form in where clauses has come up multiple times, in discussions of the where clause itself, in rust-lang/rust#20041 as a counterpart to the == constraint form, and in various proposals for negative trait reasoning (!Trait). Apr 1, 2020 · You can't constrain generic types to other types. Sep 29, 2021 · It is not possible to apply type conditional type constraints. Types have no relationship with each other. Nov 23, 2023 · Hello, While experimenting in order to better understand dynamic dispatch in Rust, I came up with the following working toy example: trait Trait { fn method(&self); } impl<T> Trait for T // where // T: std::fmt::Display, { fn method(&self) { dbg!(std::any::type_name::<Self>()); } } fn main() { let obj: &dyn Trait = &123; obj. The implementor of a trait will specify the concrete type to be used instead of the placeholder type for the particular implementation. A trait is like an interface that data types can implement. Traits can be made up of three varieties of associated items: functions and methods; types; constants; Traits may also contain additional type parameters. I can just use it as a stack allocated dynamically sized type (stack_dst). e: not implemented / a PR. system Closed June 7, 2023, 3:01am Nov 14, 2015 · It would be helpful if there were a trait like SameSize<T>: Sized implemented for all U: Sized where T and U are the same size. Consider a function such as the following: Consider a function such as the following: fn make(a: &'a u32, b: &'b u32) -> impl Trait<'a, 'b> { . The question of why a trait can't have an associated constant with a specific value is simple: just as a function definition in the trait definition is merely a default implementation and can be overridden by implementors of the trait, the value of an associated constant in the trait Sep 24, 2020 · Therefore, requiring a type to implement a trait simply means to bound (either from below or from above, I forget) the compiler's internal representation of these subtyping relationships w. Note how both the struct and the trait are parameterized on a lifetime, and that lifetime is the same. Aug 7, 2020 · I'm developing an application for STM32 cortex-m microcontrollers in Rust, using a hardware abstraction layer compliant with embedded_hal interfaces - specifically, stm32f4xx-hal. Bounds can be provided on any type in a where clause. Now, when I write: trait Copy { } I create a trait, and it defines specific behavior other types can Dec 2, 2020 · Constraints on associated trait types; If you must use generic types, Conditionally implement a Rust trait only if a type constraint is satisfied. get_element(). It has no defined values unless someone plugs a another type into it, which can be done after-the-fact. Traits may also contain additional type parameters. Feb 24, 2021 · I do disagree -- if you want a type to only hold values that satisfy a particular constraint, it's sufficient to write the constraints on the impls that actually put those values inside it. &), but you can also use it in generic constraints (which you can't do with the normal borrowing syntax). Sep 8, 2018 · The Common Rust Traits. Nov 26, 2021 · Searching online seems to always land be on the rust book (which doesn't describe something like this), rust by example, the advanced traits rust book chapter, or this webpage on traits which has a frustratingly small section on Trait constants which seems to imply this is possible, maybe. So change decode to. More ergonomic, because it: Jul 1, 2024 · Rust's generic trait constraints and trait bounds allow developers to write flexible and reusable code by defining common behavior for multiple types. Alternative to equality constraints for associated types. If you change this line: I'm new to rust and I've just learned about the Borrow trait. Try it in the Rust Playground! Jul 24, 2023 · This can be useful when working with functions or data structures that require multiple lifetimes or when defining traits with lifetime constraints. The set of traits is made up of an object safe base trait plus any number of auto traits. Improve this question. It gives you more flexibility and control over your code by enabling constraints… Oct 10, 2014 · RFC PR: rust-lang/rfcs#387; Rust Issue: rust-lang/rust#18639; Summary. This allows you to operate on values of different types in the same… If a type Item has an associated type Assoc from a trait Trait, then <Item as Trait>::Assoc is a type that is an alias of the type specified in the associated type definition. Nov 22, 2020 · Rust trait constraints are explicit, meaning you can't use something unless the constraint is there. You can use the generic trait when there is more than one output type that makes sense, for example this is legal: Rust by Example (RBE) is a collection of runnable examples that illustrate various Rust concepts and standard libraries. Mar 11, 2019 · I need to implement a trait for Vec<T> but Vec<u8> needs some special treatment. To implement your Display trait, an object may contain references but in this case their lifetime must respect this Traits. Mar 12, 2018 · A T: Trait bound on Object<T> means more than "all Object<T>s have to have T: Trait"; it actually means something like "the concept of Object<T> itself does not make sense unless T: Trait", which is a more abstract idea. Currently, closure types can be polymorphic over lifetimes. const CONST: usize = N * 4; } trait Trait { type Output; } impl<const N: usize> Trait for Foo<N> { // Used as an associated type. Dec 15, 2022 · Conditionally implement a Rust trait only if a type constraint is satisfied. See the RFC, which says:. It's too cumbersome. // (Note: `type` in this context is different from `type` when used for the form of traits, which provide static overloading and dynamic dispatch. In Dec 16, 2021 · You can accomplish this by making your own trait that takes the other traits as a bound, then add a blanket implementation for it: trait MyConstraint: Ord + Default + Clone {} impl <T: Ord + Default + Clone> MyConstraint for T {} struct LeafNode<K: MyConstraint> { keys: Vec<K> } impl<K: MyConstraint> LeafNode<K> { fn keys(&self) -> &[K] { &self Mar 20, 2020 · If you only want GameState to be implemented for a single G, you should make G an associated type of GameState instead of a generic type parameter:. Associated types connect a type placeholder with a trait such that the trait method definitions can use these placeholder types in their signatures. I added this macro add_constraint! to make syntax of adding constraints lighter. There are equivalent shorthands for many cases, but the overall requirement is that the constraints are fully Jul 24, 2023 · Traits can only require functions, associated types, and constants. the implementation only applies to types that implement the necessary traits. clone(); let _ = c. Marker traits. So in your case Oct 2, 2017 · The Add constraint on T is defined in terms of adding two &T, but these are different types (from type system perspective) than T itself. – Peter Hall Mar 13, 2020 · rust; constraints; overloading; traits; Share. Trait and lifetime bounds provide a way for generic items to restrict which types and lifetimes are used as their parameters. pub trait Decode<'a, T> { fn decode_from(&'a mut self) -> T; } And make the appropriate change to the implementation. 2. Add the ability to have trait bounds that are polymorphic over lifetimes. Defining a Trait May 7, 2019 · Well, Rust has the ability to check types at runtime - it is exposed via Any trait. In any case where T: Debug, the inherent impl kicks in and we get true. Jan 17, 2023 · A trait object using Box would be written Box<dyn Trait>. They define common behaviors that types can implement. I assumed that you want to make a function accept an optional level of "smart pointer wrapping" for a type, which is what my answer above is referring to. In the example below, we define Animal, a group of methods. But you have a trait. Here's an example in the playground. fn foo<const N: usize>() { // Cannot use in item definitions within a function body. From what I understand, the Borrow trait exposes a function borrow which works just like borrowing (i. Sep 19, 2023 · Traits are a key feature of Rust that enable abstraction and polymorphism. We need to close the gap. Follow asked Mar 13, 2020 at 1:49. 47. Motivation. API documentation for the Rust `Layout` struct in crate `tui`. Modified 4 years, 11 months ago. In my use case, it’s to ensure that a closure is the same size as () so that I don’t need to box it. Jan 2, 2019 · trait Note { type FieldsIter: Iterator<Item = Self::Item>; type Item: AsRef<str>; } I'm not a fan of this because it introduces types that at first look to be orthogonal to each other, but in the end are tightly related. Conditionally implement a Rust trait only if a type constraint is satisfied 0 How can a function require that a type implement a trait without removing the existing trait bound? Dec 21, 2017 · A good introduction can be found in the Rust book (2nd edition): Sometimes, we may want a trait to be able to rely on another trait also being implemented wherever our trait is implemented, so that our trait can use the other trait’s functionality. So you'd have to include them in the constraints anyway. AnyRefExt has is::<T>() method which is essentially the same thing as instanceof . e. If there was such thing as a conditional type in Rust, you would probably be able to describe a constraint of the form T: std::fmt::LowerHex if hex. foo2(); to be callable. You can implement any traits you like for Unsigned, like Add, Mul, etc. 0 it is still not possible but it looks like you get a nice little warning message with a description and suggested alternative. So it keeps recursing trying to see if BigNumWrapper satisfies the BigNum constraint. In fact, Rust requires that at most one implementation of a trait match for any type T. In my project, a small ray tracer, I have a vertex type that has a position and a normal. The Num trait is implemented for all numeric types. where can be used for constraints with traits: Nov 4, 2015 · The issue is that the implementation of Iterator requires a constraint to Num, but I don't know how to express this: impl <T : Num> Iterator for Fib<T> { } Produces: use of undeclared trait name `Num` And when I try either use std::num::{Num} or use num::traits::{Num}, I am told that the modules do not exist. clone(); } Feb 21, 2023 · Edit: I missed that you have a trait Tr. What it has is a way to define constraints. This ensures your generic type T has all of the expected numeric operators, Add, Sub, Mul, Div, Rem, can be partially equality checked via PartialEq, it also exposes a value for 1 and 0 for T. 1. weeef tewazw qamkkqf clwgra bypp hojviyh xwdoqk ipxnlq yrxqhd hhuagge